Springer, 2019. — 328 p. — (Birkhäuser Advanced Texts Basler Lehrbücher). — ISBN: 3030118029. This book explains the foundations of holomorphic curve theory in contact geometry. By using a particular geometric problem as a starting point the authors guide the reader into the subject. As such it ideally serves as preparation and as entry point for a deeper study of the analysis...
Springer, India, 2016. — 628 p. — ISBN10: 8132228413 Discusses the basic concepts of algebraic topology with numerous related illustrations and applications Approaches the topic nearly “from scratch” and accompanies students through its natural development Provides examples and step-by-step instructions and explains problem-solving techniques for a better grasp of the topic...
Oxford University Press, UK, 2016. — 275 p. — (Oxford Graduate Texts in Mathematics 25) — ISBN10: 0198784864 This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut. The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to...
Springer, 2014. — 595 p. — (Universitext). — ISBN: 978-1-4471-5495-2. This book is devoted to the solution of one of these problems, a famous conjecture due to Arnold, which proposes to give a lower bound for the number of periodic trajectories of a Hamiltonian system using an invariant that depends only on the topology of the symplectic manifold on which this system evolves....
Cambridge University Press, 2022. — 356 p. — (London Mathematical Society Lecture Note Series 474). — ISBN 9781108931946. This volume contains eight research papers inspired by the 2019 'Equivariant Topology and Derived Algebra' conference, held at the Norwegian University of Science and Technology, Trondheim in honour of Professor J. P. C. Greenlees' 60th birthday. These...
New York, Amsterdam: W.A. Benjamin, Inc., 1968. — 762 p. This book is based on a course I gave at Columbia University in 1966-67. Its writing was greatly facilitated by the notes for that course which were taken by Tsit-Yuen Lam, M. Pavaman Murthy, and Charles Small. I am extremely grateful to them for their assistance and criticism. I had originally hoped to make the...
World Scientific, 1999. — 622 p. The conference was comprised of a workshop that explained the fundamentals of the field for young scholars thinking of dipping into it, and a symposium in which research mathematicians presented recent results. The six expository lectures, one in French, include discussions of hypoelliptic operators, algebraic geometry, and values of zeta...
Springer, 1986. — 346 p. — (Mathematical Sciences Research Institute Publications 05). — ISBN13: 978-1-4613-9574-4. K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to...
Cham: Springer, 2021. — 217 p. This book gives a brief treatment of the equivariant cohomology of the classical configuration space F(ℝ^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and progressing through the work of Fox and Neuwirth (1962), Fadell and...
Springer, Amer. Math. Soc., 2000. — 106 p. — (CRM Monograph Series. Book 11) — ISBN: 0821821148 Work of Borel on higher regulators for number fields is discussed. The Borel regulator for K3 of a number field is described explicitly in terms of the dilogarithm function. A generalization, based on functions related to the dilogarithrn and to the Dedekind 7]-function, leads to a...
Princeton: Princeton University Press, 1954. — 205 p. Frontmatter Riemannian Manifold Harmonic and Killing Vectors Harmonic and Killing Tensors Harmonic and Killing Tensors in Flat Manifolds Deviation from Flatness Semi-simple Group Spaces Pseudo-harmonic Tensors and Pseudo-Killing Tensors in Metric Manifolds with Torsion Kaehler Manifold Supplements Backmatter
Springer, 1982. — 339 p. — ISBN: 0387906134. The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology. Accord ingly, we move primarily in the realm of smooth manifolds and use the de Rham theory as a prototype of all of cohomology. For applications to homotopy theory we also discuss by way...
Springer, 1982. — 351 p. — (Graduate Texts in Mathematics 82). — ISBN: 0387906134. The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology. Accord ingly, we move primarily in the realm of smooth manifolds and use the de Rham theory as a prototype of all of cohomology. For applications to...
New York: Springer, 2021. — 215 p. — ISBN10 3030706079. — ISBN13 978-3030706074. Algebraic Topologyis an introductory textbook based on a class for advanced high-school students at the Stanford University Mathematics Camp (SUMaC) that the authors have taught for many years. Each chapter, or lecture, corresponds to one day of class at SUMaC. The book begins with the...
Boston: Birkhauser. - 1993. - 320 p. (Progress in Mathematics. Volume 107) haracteristic classes are certain cohomology classes associated either to a vector bundle or a principal bundle over a manifold. In the past 25 years, characteristic classes have been used to construct some of the basic objects in infinite-dimensional geometry and loop groups, geometric quantization,...
Published online. — 101 p. English. Abstract. In this book we give a complete proof of the fact that Borel’s regulator map is twice Beilinson’s regulator map. The strategy of the proof follows the argument sketched in Beilinson’s original paper and relies on very similar descriptions of the Chern–Weil morphisms and the van Est isomorphism. The book also reviews some material...
Springer, 2024. — 500 p. This is the sixth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. Singularities are ubiquitous in mathematics and science in general, and singularity theory is a crucible where...
American Mathematical Society, 2021. — 367 p. — (Mathematical Surveys and Monographs 264). — ISBN 9781470466718. This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum...
Singapore: World Scientific Publishing Company, 2011. — 294 p. The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology. This example is a gateway to a new idea of higher dimensional algebra in which diagrams replace algebraic expressions and relationships between diagrams...
Springer, 2019. — 442 p. — (Springer Monographs in Mathematics). — ISBN: 978-3-030-33241-9. The primary aim of this monograph is to achieve part of Beilinson’s program on mixed motives using Voevodsky’s theories of A1-homotopy and motivic complexes. Historically, this book is the first to give a complete construction of a triangulated category of mixed motives with rational...
Springer, 2022. — 822 p. — ISBN-13 9783030957599. — ISBN-10 3030957594. This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth...
New York, USA: Science Publishing Group, 2017. — 288 p. – ISBN: 978-1-940366-79-1. The book consists of two parts. Part I is an axiomatic frame for the K-theory for C*-algebras. Some central results of this theory are heaved to the status of axioms and the other results are then derived from these axioms. In Part II the author constructs an example for this axiomatic theory...
Cambridge: Cambridge University Press, 2011. — 383 p. Fusion systems are a recent development in finite group theory and sit at the intersection of algebra and topology. This book is the first to deal comprehensively with this new and expanding field, taking the reader from the basics of the theory right to the state of the art. Three motivational chapters, indicating the...
Springer International Publishing AG, 2017. — 325 p. — (Oberwolfach Seminars 47) — ISBN: 978-3-319-59914-4. This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is...
American Mathematical Society, 2009. — 468 p. — (Graduate Studies in Mathematics. Volume 106). A topological embedding is a homeomorphism of one space onto a subspace of another. The book analyzes how and when objects like polyhedra or manifolds embed in a given higher-dimensional manifold. The main problem is to determine when two topological embeddings of the same object are...
Providence: American Mathematical Society, 2001. — 383 p. The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help...
Princeton University Press, 2008. — xvi+684 p. — (London Mathematical Society monographs series, 32). — ISBN: 978-0-691-13138-2. The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples...
Springer, 2014. — 240 p. — (Universitext). — ISBN: 1441979093, 9781441979094, 9781441979100
A Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years with growing applications in math, computer science, and other...
2nd Edition. — Springer Nature Singapore and Hindustan Book Agency, 2018. — 355 p. — (Texts and Readings in Mathematics 27). — ISBN: 978-981-10-8734-9. This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail....
European Mathematical Society, 2008. — 580 p. — (EMS Textbooks in Mathematics) — ISBN: 9783037190487. Algebraic topology is the interplay between “continuous” and “discrete” mathematics. Continuous mathematics is formulated in its general form in the language of topological spaces and continuous maps. Discrete mathematics is used to express the concepts of algebra and...
De Gruyter, 2021. — 391 p. This book provides an introduction to topological groups and the structure theory of locally compact abelian groups, with a special emphasis on Pontryagin-van Kampen duality, including a completely self-contained elementary proof of the duality theorem. Further related topics and applications are treated in separate chapters and in the appendix....
Berlin: Walter de Gruyter, 2024. - 418 p. - ISBN 3111517365. The aim of the textbook is two-fold: first to serve as an introductory graduate course in Algebraic Topology and then to provide an application-oriented presentation of some fundamental concepts in Algebraic Topology to the fixed point theory . A simple approach based on point-set Topology is used throughout to...
Walter de Gruyter, 2024. — 418 p. — ISBN: 978-3-11-151778-0. The aim of the textbook is two-fold: first to serve as an introductory graduate course in Algebraic Topology and then to provide an application-oriented presentation of some fundamental concepts in Algebraic Topology to the fixed point theory . A simple approach based on point-set Topology is used throughout to...
Walter de Gruyter, 2024. — 418 p. — ISBN: 978-3-11-151778-0. The aim of the textbook is two-fold: first to serve as an introductory graduate course in Algebraic Topology and then to provide an application-oriented presentation of some fundamental concepts in Algebraic Topology to the fixed point theory . A simple approach based on point-set Topology is used throughout to...
Walter de Gruyter, 2024. — 418 p. — ISBN: 978-3-11-151778-0. The aim of the textbook is two-fold: first to serve as an introductory graduate course in Algebraic Topology and then to provide an application-oriented presentation of some fundamental concepts in Algebraic Topology to the fixed point theory . A simple approach based on point-set Topology is used throughout to...
Kluwer Academic Publishers, 1997, 405 pages This book arose from courses taught by the authors, and is designed for both instructional and reference use during and after a first course in algebraic topology. It is a handbook for users who want to calculate, but whose main interests are in applications using the current literature, rather than in developing the theory. Typical...
Springer, 1980. — 379 p. — Series: Classics in Mathematics. ISBN10: 3540586601 ISBN13: 978-3540586609. Springer is reissuing a selected few highly successful books in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. Springer-Verlag began publishing books in higher mathematics in 1920. This is a reprint of...
Springer, 1973. — 548 p. A conference on algebraic K-theory was held at the Battelle Seattle Research Center from August 28 to September 8, 1972, with the joint support of the National Science Foundation and the Battelle Memorial Institute. The present volume consists mainly of papers presented at, or stimulated by, that conference, plus some closely related papers by...
Princeton, New Jersey, USA: Princeton University Press, 1952. — 345 p. — (Princeton Mathematical Series 18). The principal contribution of this book is an axiomatic approach to the part of algebraic topology called homology theory. It is the oldest and most extensively developed portion of algebraic topology, and may be regarded as the main body of the subject. The present...
American Mathematical Society, USA, 2017. — 202 p. — (Contemporary Mathematics 689) — ISBN10: 1470428474. This volume contains the proceedings of the AMS Special Session on Algebraic and Combinatorial Structures in Knot Theory and the AMS Special Session on Spatial Graphs, both held from October 24-25, 2015, at California State University, Fullerton, CA.Included in this volume...
Springer-Verlag Berlin Heidelberg, 2005. — 1177 p. — ISBN10: 3-540-230-19-X, ISBN13: 978- 3-540-23019-9 This handbook offers a compilation of techniques and results in K-theory These two volumes consist of chapters, each of which is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished...
Springer, 2010. — 264 p. Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in...
Springer, 2020. — 138 p. — (SpringerBriefs in Mathematics). — ISBN: 978-981-15-3346-4. Is the first introductory textbook for the Iitaka conjecture Gives a simple new proof of Viehweg's conjecture for fiber spaces whose geometric generic fiber is of general typeProvides a very accessible account for Viehweg's theory of weakly positive sheaves and big sheaves About this book The...
2nd edition. — Wien: Springer, 2009. — 446 p. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential...
Springer-Verlag London Limited, 2011. — 415 p. — (Algebra and Applications 15) — ISBN: 0857297155. The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of...
CreateSpace, 2014. — 265 p. This text gives a brisk and engaging introduction to the mathematics behind the recently established field of Applied Topology. Over a century of development of principles and techniques in algebraic topology has of late crossed over to a variety of application domains. This text gives a completely novel introduction to these methods in the context...
3rd Edition. — Cambridge University Press, 2010. — 273 p. — ISBN13: 978-0-511-90219-2. Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere,...
Oxford: Oxford University Press, 1996. — 278 p. This highly readable text details the interaction between the mathematical theory of knots and the theories of surfaces and group presentations. It expertly introduces several topics critical to the development of pure mathematics while providing an account of math "in action" in an unusual context. The authors skillfully combine...
Singapore: World Scientific, 2022. — 372 p. Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying...
Cambridge University Press, 2009. — 444 p. — (New Mathematical Monographs: 13). This is the first authored book to be dedicated to the new field of directed algebraic topology that arose in the 1990s, in homotopy theory and in the theory of concurrent processes. Its general aim can be stated as 'modelling non-reversible phenomena' and its domain should be distinguished from...
Springer, 2019. — 88 p. — (SpringerBriefs in Mathematics). — ISBN10: 3319994883. This volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven strings is computed using a wide variety of tools. Many of the techniques extend to the general case, and the...
Paris: Societe Mathematique De France, 2016. — 142 p. Sheaves on manifolds are perfectly suited to treat local problems, but many spaces one naturally encounters, especially in Analysis, are not of local nature. The subanalytic topology (in the sense of Grothendieck) on real analytic manifolds allows one to partially overcome this difficulty and to define for example sheaves of...
Cornell University, 2018. — 559 p. In most major universities one of the three or four basic first-year graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. Note : This is the latest and up-to-date electronic...
A. Hatcher, 2000. — 553 Pages.
This book was written to be a readable introduction to Algebraic Topology with rather broad coverage of the subject. Our viewpoint is quite classical in spirit, and stays largely within the confines of pure Algebraic Topology. In a sense, the book could have been written thirty years ago since virtually all its content is at least thatold. However,...
A. Hatcher, 2000. — 553 p. This book was written to be a readable introduction to Algebraic Topology with rather broad coverage of the subject. Our viewpoint is quite classical in spirit, and stays largely within the confines of pure Algebraic Topology. In a sense, the book could have been written thirty years ago since virtually all its content is at least thatold. However, the...
Allen Hatcher, 2001. - 99 pages. Chapter 1, containing basics about vector bundles. Part of Chapter 2, introducing K-theory, then proving Bott periodicity in the complex case and Adams\' theorem on the Hopf invariant, with its famous applications to division algebras and parallelizability of spheres. Not yet written is the proof of Bott Periodicity in the real case, with its...
Boston: de Gruyter, 2018. — 359 p. This authoritative book on periodic locally compact groups is divided into three parts: The first part covers the necessary background material on locally compact groups including the Chabauty topology on the space of closed subgroups of a locally compact group, its Sylow theory, and the introduction, classifi cation and use of inductively...
Cambridge: Cambridge University Press, 1971. — 107 p. These notes constitute a faithful record of a short course of lectures given in São Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give...
European Mathematical Society, 2006. — 226 p. — ISBN: 3037190116. Dynamics on the Riemann Sphere presents a collection of original research articles by leading experts in the area of holomorphic dynamics. These papers arose from the symposium Dynamics in the Complex Plane, held on the occasion of the 60th birthday of Bodil Branner. Topics covered range from Lattès maps to...
Ithaka: Matrix Press, 2006. — 482 p. In the first volume I have given quite a complete treatment of Teichmuller theory. Of course I have collected the material that will be needed in the second volume, but I have also proved a number of other results that struck me as interesting in themselves and in the spirit of the book, such as the universal property of Teichmuller spaces,...
Matrix Editions, 2016. — 181 p. The second of four volumes devoted to Teichmuller theory and its applications to geometry, topology, and dynamics, this volume proves two theorems by William Thurston: the classification of homeomorphisms of surfaces and the topological characterization of rational maps.
Cambridge University Press, 1992. — 186 p. — (Cambridge Studies in Advanced Mathematics 29). — ISBN13: 9780521375108. In this graduate textbook Professor Humphreys presents a concrete and up-to-date introduction to the theory of Coxeter groups. He assumes that the reader has a good knowledge of algebra, but otherwise the book is self contained. The first part is devoted to...
American Mathematical Society, 2013. — 454 p. — (Mathematical Surv. Monogr. 185). — ISBN: 0821891316. At the end of the last century, differential geometry was challenged by theoretical physics: new objects were displaced from the periphery of the classical theories to the center of attention of the geometers. These are the irrational tori, quotients of the 2-dimensional torus...
World Scientific, 2021. — xiv, 357 p. — ISBN 978-981-122-275-7, 978-981-122-276-4, 978-981-122-277-1. The D(2) problem is a fundamental problem in low dimensional topology. In broad terms, it asks when a three-dimensional space can be continuously deformed into a two-dimensional space without changing the essential algebraic properties of the spaces involved. The problem is...
Cham: Springer, 2025. — 438 p. Preface Acknowledgments Introduction Riemann Surfaces, Braids, Mapping Classes, and Teichmüller Theory Free Homotopy Classes of Mappings and Conjugacy Classes of Group Elements Riemann Surfaces Braids Mapping Class Groups The Relation Between Braids and Mapping Classes Beltrami Differentials and Quadratic Differentials Elements of Teichmüller...
2000. — 219 p. This book presents a novel approach to homology that emphasizes the development of efficient algorithms for computation. As well as providing a highly accessible introduction to the mathematical theory, the authors describe a variety of potential applications of homology in fields such as digital image processing and nonlinear dynamics. The material is aimed at a...
Birkhäuser, 2022. — 184 p. — (Compact Textbooks in Mathematics). — ISBN 3030983129. This textbook provides a succinct introduction to algebraic topology. It follows a modern categorical approach from the beginning and gives ample motivation throughout so that students will find this an ideal first encounter to the field. Topics are treated in a self-contained manner, making...
Societe Mathematique de France, 1997. — 121 p.
This book provides a concise introduction to quantum groups, braided monoidal categories, and quantum invariants of knots and of three-dimensional manifolds. The exposition emphasizes the newly discovered deep relationships between these areas.
Introduction
The Yang-Baxter Equation and Braid Group Representations
The...
Mineola, New York, USA: Dover Publications, Inc., 2018. — 96 p. — ISBN: 129785148X. A great researcher, writer, and teacher in an era of tremendous mathematical ferment, Felix Klein (1849-1925) occupies a prominent place in the history of mathematics. His many talents included an ability to express complicated mathematical ideas directly and comprehensively, and this book, a...
De Gruyter, 2024 — 248 p. — (De Gruyter Textbook). — ISBN 978-3111014852. This book is ideal as an introduction to algebraic topology and applied algebraic topology featuring a streamlined approach including coverage of basic categorical notions, simplicial, cellular, and singular homology, persistent homology, cohomology groups, cup products, Poincare Duality, homotopy theory,...
World Scientific, 2015. — 222 p. Preface Smooth Morse Theory First Steps Fundamental Results in Morse Theory Topological Consequences Homology Piecewise Linear Morse Theory Discrete Morse Theory First Steps Topological Consequences Algorithms Applications Appendix A. Smooth Manifolds Appendix B. Cell Complexes Bibliography Index Back Cover
Springer, 1990. — 338 p. A central problem in algebraic topology is the calculation of the values of the stable homotopy groups of spheres +*S. In this book, a new method for this is developed based upon the analysis of the Atiyah-Hirzebruch spectral sequence. After the tools for this analysis are developed, these methods are applied to compute inductively the first 64 stable...
Cambridge University Press. Cambridge, UK; New York, NY, USA. 1980. First published. 280 pages. Includes index. ISBN: 0521298644, 0521231957; ISBN13: 9780521298643, 9780521231954. This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three...
Springer, 2008. — 399 p. The intent of this book is to introduce the reader to the beautiful world of Combinatorial Algebraic Topology. While the main purpose is to describe the modern research tools and latest applications of this field, an attempt has been made to keep the presentation as self-contained as possible. The text is divided into three major parts, which provide...
Basel: Birkhäuser, 2000. — 436 p. This volume presents the invited lectures of a conference devoted to Infinite Length Modules, held at Bielefeld, September 7-11, 1998. Some additional surveys have been included in order to establish a unified picture. The scientific organization of the conference was in the hands of K. Brown (Glasgow), P. M. Cohn (London), I. Reiten...
Basel: Birkhäuser, 2005. — 267 p. These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the...
Harvard University, 2018. — 314 p. The first part of the course will be dedicated to studying the appropriate class of algebraic invariants of spaces; the generalized cohomology theories. One of the important properties of generalized cohomology theories is that they are homotopy-invariant, that is, send homotopy equivalences to isomorphism. Thus they factor of over the homotopy...
Springer International Publishing AG, 2017. — 481 p. — (Springer Proceedings in Mathematics & Statistics 219) — ISBN: 3319681028. This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete...
Springer International Publishing AG, 2017. — 481 p. — (Springer Proceedings in Mathematics & Statistics 219) — ISBN: 3319681028. This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete...
European Mathematical Society, 2015. — 500 p. — (IRMA Lectures in Mathematics and Theoretical Physics 24). — ISBN: 978-3-03719-153-8. In the late 1990s two initially unrelated developments brought free loop spaces into renewed focus. In 1999, Chas and Sullivan introduced a wealth of new algebraic operations on the homology of these spaces under the name of string topology, the...
Paperback ed. — Oxford: Oxford University Press, 2006. — 408 p. — (Oxford Graduate Texts in Mathematics, Book 9). — ISBN: 978-0199202485, 0199202486. This new-in-paperback introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and projects, which fosters a teaching style that encourages the student...
Springer, 2007. — 252 p. — (Springer Monographs in Mathematics). — ISBN: 3540368221. Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this...
Springer, 2002. — 612 p. In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information...
Springer, 1989. — 457 p. The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the...
Cambridge: Cambridge University Press, 1997. — 292 p. De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of...
Newcastle upon Tyne: Cambridge Scholars Publishing, 2022. — 107 p. Algebraic topology is a fascinating and dynamic field at the crossroads of topology and algebra, both pure and applied. This volume is the first comprehensive, book-form treatment of the subject. It provides a swift walk through the main basic tools of algebraic topology, including homology and homotopy groups,...
Springer, 2020. — 453 p. — (Springer Monographs in Mathematics). — ISBN: 978-3-030-43104-4. This book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous.They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however elementary they may be, is formidable....
Springer. New York, NY, USA. 1991. 428 pages. ISBN: 038797430X, 354097430X
This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are: the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. The text consists of material from the...
Springer. New York, NY, USA. 1991. 428 pages. ISBN: 038797430X, 354097430X
This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are: the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. The text consists of material from the...
European Mathematical Society, 2006. — 107 p. — (EMS Series of Lectures in Mathematics 03) — ISBN: 3-03719-023-X. Algebraic topology is the study of geometric objects via algebraic methods. Familiarity with its main ideas and methods is quite useful for all undergraduate and graduate students who specialize in any of the many branches of mathematics and physics that have...
University Of Chicago Press, 2012. - 544 pages. With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology...
Springer, 2019. — 127. — (SpringerBriefs in Mathematics). — ISBN: 978-3-030-18155-0. This is an in-depth report on the endotrivial modules, an important class of modular representations for finite groups. Following the historical development of the theory, the book starts with a review of the necessary definitions and some key examples. The main results obtained using...
2nd edition. — Cambridge University Press 2001. — 576 p. — ISBN13: 978-0521567596, ISBN10: 0521567599. Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for...
Providence, Rhode Island: American Mathematical Society, 1994. — viii+210 p. — ISBN: 0-8218-0332-8. J -holomorphic curves revolutionized the study of symplectic geometry when Gromov first introduced them in 1985. Through quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics. This book presents the first coherent and full...
Providence, Rhode Island: American Mathematical Society, 1994. — 210 p. — ISBN: 0-8218-0332-8. J-holomorphic curves revolutionized the study of symplectic geometry when Gromov first introduced them in 1985. Through quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics. This book presents the first coherent and full...
Providence, Rhode Island: American Mathematical Society, 2004. — 670 p. — ISBN: 0-8218-3485-1. The theory of J-holomorphic curves has been of great importance since its introduction by Gromov in 1985. In mathematics, its applications include many key results in symplectic topology. It was also one of the main inspirations for the creation of Floer homology. In mathematical...
Providence, Rhode Island: American Mathematical Society, 2004. — xii+670 p. — ISBN: 0-8218-3485-1 The theory of J-holomorphic curves has been of great importance since its introduction by Gromov in 1985. In mathematics, its applications include many key results in symplectic topology. It was also one of the main inspirations for the creation of Floer homology. In mathematical...
World Scientific, 2021. — 405 p. Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in...
MDPI, 2019. — 160 p. — ISBN 978-3-03897-644-8, 978-3-03897-645-5. This volume on topological groups, called “Topological Groups: Advances, Surveys, and Open Questions”, contains recent articles by some of the best scholars in the world on topological groups including Taras Banakh, Michael Megrelishvili, George A. Willis, and O’lga V. Sipacheva, as well as a paper by the...
Longman Scientific & Technical, 1987. — 213 p. Preface. Introduction. Branched coverings of complex manifolds. Definition of branched coverings of complex manifolds. Construction of maximal branched coverings of non-singular type. Construction of maximal branched coverings (general case). Examples of finite branched coverings. Fenchel's problem. Fields of algebraic functions....
Springer, 2007. — 252 p. — (Universitext). — ISBN13: 978-0-387-49509-5. This self-contained treatment of Morse Theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part contains the foundations of Morse theory (over the reals). The second part consists of...
2nd Edition. — Springer, 2011. — 366 p. — (Universitext). — ISBN: 9781461411055. This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part contains the foundations of Morse theory. The second part consists of...
Cambridge University Press, UK, 2015. — 421 p. — (new mathematical monographs 28) — ISBN: 110707245X Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 1 covers the basic materials of...
Cambridge University Press, UK, 2015. — 471 p. — (new mathematical monographs 29) — ISBN: 1107109671 Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 2 provides a comprehensive introduction...
Cambridge University Press, UK, 2008. — 220 p. — (Cambridge Studies in Advanced Mathematics 111) — ISBN13: 978-0-511-38668-8. Topological K-theory first appeared in a 1961 paper by Atiyah and Hirzebruch; their paper adapted the work of Grothendieck on algebraic varieties to a topological setting. Since that time, topological K-theory (which we will henceforth simply call...
Springer, 2020. — viii, 213 p. — (Lecture Notes in Mathematics, 2262 / History of Mathematics Subseries, 2262). — ISBN: 978-3-030-43995-8, 978-3-030-43996-5. True PDF These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during 1979-1980. He had just received the Fields Medal for...
Providence, Rhode Island: American Mathematical Society, 2018. — xiii+149 p. — (University lecture series, vol. 70). — ISBN: 978-1-4704-4115-9. Within the subject of topological dynamics, there has been considerable recent interest in systems where the underlying topological space is a Cantor set. Such systems have an inherently combinatorial nature, and seminal ideas of...
Berlin: Springer, 1994. — 405 p. Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the...
Springer-Verlag, 1988. — 447 p. — (Graduate Texts in Mathematics 119). — ISBN13: 978-1-4612-8930-2. There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to J. H. C. Whitehead. Of course, this is false, as a glance at the books of Hilton and Wylie, Maunder, Munkres, and Schubert reveals....
American Mathematical Society, 2019. — 289 p. — (Student Mathematical Library 90). — ISBN13: 9781470453794. Discrete Morse theory is a powerful tool combining ideas in both topology and combinatorics. Invented by Robin Forman in the mid 1990s, discrete Morse theory is a combinatorial analogue of Marston Morse's classical Morse theory. Its applications are vast, including...
Tokyo: The Mathematical Society of Japan, 2010. — 227 p. n this book we study three important classes of infinite-dimensional Kähler manifolds — loop spaces of compact Lie groups, Teichmüller spaces of complex structures on loop spaces, and Grassmannians of Hilbert spaces. Each of these manifolds has a rich Kähler geometry, considered in the first part of the book, and may be...
CRC Press, 2013. — 548 p. — ISBN: 9781466562431 Building on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell...
Sringer, 2019. — 318 p. — (Trends in Mathematics). — ISBN10: 9811357412. This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of...
New York: Springer, 1994. — 273 p. Intended for use both as a text and a reference, this book is an exposition of the fundamental ideas of algebraic topology. The first third of the book covers the fundamental group, its definition and its application in the study of covering spaces. The focus then turns to homology theory, including cohomology, cup products, cohomology...
Paris: Société Mathématique de France, 2018. — 116 p. Acknowledgements Preliminaries and Notation Motivic complexes I The construction The p-parts Finite coefficients The p-completed parts The completed part The rational parts The definition Motivic Complexes II A strictification Properties of the motivic complexes Comparison to flat maps Some localization triangles The étale...
Cambridge: Cambridge University Press, 2021. — 234 p. The theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond relaxing conditions on liftings of homomorphisms. This has set...
Reprint of the 1975 edition. — Springer-Verlag, 2002. — 526 p. — (Classics in Mathematics). — ISBN-13 9783540427506. This book is the result of lecture courses on algebraic topology given by the author at the University of Manchester in 1967-1970, at Cornell University in 1970-1971 and at the Georg August University, Gottingen, in 1971-1972. The level of the material is more...
Paris: European Mathematical Society, 2018. — 161 p. — (Zurich Lectures in Advanced Mathematics). — ISBN: 9783037191897, 3037191899. Coxeter groups are groups generated by reflections, and they appear throughout mathematics. Tits developed the general theory of Coxeter groups in order to develop the theory of buildings. Buildings have interrelated algebraic, combinatorial and...
Princeton University Press, 2020. — 338 p. — (Annals of Mathematics Studies, 204) — ISBN: 9780691191744, 9780691191751, 9780691197487. This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of...
W.A. Benjamin, Inc., New York, USA, 1970, 1998. — 288 p. — ISBN: 0486462390. The motivation for singular homology lies in the fact that certain topological spaces can be distinguished from each other (i.e., can be shown to be nonhomeomorphic) because every closed curve on one forms the boundary of a surface in that space, while this property is not satisfied by the other space....
W.A. Benjamin, Inc., New York, USA, 1970, 1998. — 288 p. — ISBN: 0486462390. The motivation for singular homology lies in the fact that certain topological spaces can be distinguished from each other (i.e., can be shown to be nonhomeomorphic) because every closed curve on one forms the boundary of a surface in that space, while this property is not satisfied by the other space....
Springer, 2014. — 169 p. — (Graduate Texts in Mathematics 270). — ISBN: 978-1-4939-1843-0. This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are...
Springer, 2018. — 303 p. — (Lecture Notes in Mathematics 2216). — ISBN: 3319913697. This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the...
Пер. с англ. М.: Мир, 1982. - 200 с.
Краткое введение в теорию бесконечнократных пространств петель - новое направление современной топологии. Автор книги - известный английский математик.
Для математиков разных специальностей, аспирантов и студентов.
М.: Мир, 1967. - 258 с.
От издательства:
Лекции известного английского математика Майкла Фрэнсиса Атья, удостоенного Филдсовской медали в 1966 г., посвящены одному из самых мощных средств современной алгебраической топологии - теории К-функтора. С помощью этой теории недавно были решены многие трудные задачи из разных областей математики.
Понятие К-функтора возникло в самое...
М.: Мир, 1967. — 259 c. Лекции известного английского математика Майкла Фрэнсиса Атья, удостоенного Филдсовской медали в 1966 г., посвящены одному из самых мощных средств современной алгебраической топологии - теории К-функтора. С помощью этой теории недавно были решены многие трудные задачи из разных областей математики. Понятие К-функтора возникло в самое последнее время и...
М.: Независимый Московский университет (НМУ), Московский центр непрерывного математического образования (МЦНМО), 2002 — 61 с. Основным предметом нашего изучения являются поверхности в трёхмерном евклидовом пространстве, главным образом, компактные не имеющие края. Мы начнём со случая, когда поверхность расположена в пространстве с самопересечениями, но без локальных...
Перевод с английского А. В. Михалева под ред. Е. С. Голода. — М.: Мир, 1973. — 602 с. В монографии известного американского математика X. Басса — одного из создателей алгебраической K-теории — дано первое систематическое изложение этой теории. Материал изложен тщательно и подробно, с большим педагогическим мастерством. В вводной части приведены необходимые алгебраические...
Перевод с английского А. В. Михалева под ред. Е. С. Голода. — М.: Мир, 1973. — 602 с. В монографии известного американского математика X. Басса — одного из создателей алгебраической K-теории — дано первое систематическое изложение этой теории. Материал изложен тщательно и подробно, с большим педагогическим мастерством. В вводной части приведены необходимые алгебраические...
Издательство "МИР", Москва 1971.-291 с. Систематическое изложение теории ретрактов, принадлежащее создателю этой теории - крупному польскому математику К. Борсуку. Теория ретрактов - важный раздел современной топологии, лежащий на стыке общей и алгебраической топологии. В конце книги дан обзор нерешенных проблем. Изложение ясное, доступное и в то же время весьма компактное....
М.: Мир. 1976. 194с.
Имя известного польского математика К. Борсука знакомо советскому читателю по переводу его книги «Теория ретрактов» («Мир», 1971). Новая работа К. Борсука посвящена теории шейпов — интересному направлению теории гомотопий, которое возникло буквально в последние годы и представляет собой дальнейшее, развитие теории ретрактов. За создание этой теории К. Борсук...
Итоги науки и техники. М.: ВИНИТИ, 1988. - 246 с.
Алгебраическая топология, находившаяся в сороковые — шестидесятые годы нашего века в фазе интенсивного развития, достигла к настоящему времени относительно стабильного состояния. При этом в ней четко обозначились границы круга понятий и фактов, представляющих общематематический интерес. В то же время область применений топологии...
В монографии Р. Годемана дается систематическое изложение области современной топологии — теории пучков. Эта теория является мощным аппаратом исследования в различных областях современной алгебры, геометрии и анализа.
Книга рассчитана на математиков — научных работников, аспирантов и студентов старших курсов.
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Предисловие автора
Указания автора
Глава...
Этот курс алгебраической топологии и теории многообразий. В книге простота и ясность подачи материала. Большое количество интересных примеров. Элементарное и доступное изложение топологии многообразий. Книга рассчитана на широкий круг математиков и вполне пригодна как начальный учебник по алгебраической топологии для студентов и аспирантов университетов и пединститутов. Страниц...
Электронное издание. — М.: МЦНМО, 2014. — 366 с. — ISBN: 978-5-4439-2156-3. Книга посвящена задаче о топологической сопряжённости отображений. В монографии приводится её алгоритмическое решение для обобщённых псевдоаносовских гомеоморфизмов как ориентируемых, так и неориентируемых поверхностей. Это решение основано на рассмотрении марковских разбиений некоторого специального...
Перевод с английского Ю. П. Соловьева под ред. А. С. Мищенко. М.: Мир, 1981, - 360 с. Написанная французским математиком книга вводит читателя в новое направление алгебраической топологии. Изложение отличается от имеющихся полнотой и систематичностью. Весьма ценны многочисленные конкретные вычисления К-групп. Даны важнейшие приложения К-теории (инварианты Хопфа, векторные поля,...
М.: МЦНМО, 2014. — 422 с. — ISBN: 978-5-4439-0245-6. Книга посвящена увлекательному и актуальному разделу математики — теории кос, сочетающей богатство чисто алгебраической структуры и тесные связи с важными разделами маломерной топологии, в частности, с теорий узлов и зацеплений. В данной монографии, помимо прочего, обсуждаются такие недавние результаты, как точность...
М.: МЦНМО, 2014. — 422 с. — ISBN: 978-5-4439-0245-6. Книга посвящена увлекательному и актуальному разделу математики — теории кос, сочетающей богатство чисто алгебраической структуры и тесные связи с важными разделами маломерной топологии, в частности, с теорий узлов и зацеплений. В данной монографии, помимо прочего, обсуждаются такие недавние результаты, как точность...
Пер. с англ. В. Быков, Евгений Скляренко. — М.: Мир, 1983. — 302 с. — (Современная математика. Вводные курсы). "Вводный курс алгебраической топологии, написанный английским математиком. Изложение сопровождается большим количеством примеров и рисунков, дано около 350 упражнений для самостоятельной проработки. Для математиков различных специальностей, аспирантов и студентов,...
Пер. с англ. В. Быков, Евгений Скляренко. — М.: Мир, 1983. — 302 с. — (Современная математика. Вводные курсы). "Вводный курс алгебраической топологии, написанный английским математиком. Изложение сопровождается большим количеством примеров и рисунков, дано около 350 упражнений для самостоятельной проработки. Для математиков различных специальностей, аспирантов и студентов,...
Пер. с англ. М.Р. Шура-Бура. — Предисл. П.С. Александрова. — М.: Иностранная литература, 1949. — 505 с. Предлагаемая вниманию читателя книга принадлежит перу одного из крупных современных геометров, С. Лефшеца,- основные работы которого относятся к алгебраической геометрии и к топологии. Обе главнейшие специальности Лефшеца тесно переплетаются между собой: в алгебраической...
М.: Мир, 1977, - 344 с. Книга, в которой объединены две монографии, может служить хорошим введением в алгебраическую топологию. В первой ее части, написанной У. Масси, подробно рассматриваются фундаментальная группа и основные понятия топологии — накрывающие пространства, двумерные многообразия, CW-комплексы, приводятся многочисленные примеры и устанавливаются связи с теорией...
М.: Мир, 1977. — 344 с. Книга, в которой объединены две монографии, может служить хорошим введением в алгебраическую топологию. В первой ее части, написанной У. Масси, подробно рассматриваются фундаментальная группа и основные понятия топологии — накрывающие пространства, двумерные многообразия, CW-комплексы, приводятся многочисленные примеры и устанавливаются связи с теорией...
М.: МЦНМО, 2007. — 454 с. В книге изложены основы алгоритмической и компьютерной топологии трехмерных многообразий, включая теорию сложности, теорию нормальных поверхностей и алгоритмическую классификацию большого числа трехмерных многообразий. В частности, это дает полную классификацию классических узлов. Книга адресована широкому кругу специалистов в области математики и тех...
Учебное пособие для вузов. - Ижевск, Регулярная и хаотическая динамика, 2003. - 128 с. (Серия: Современная математика)
Рекомендовано Научно-методическим советом по математике Министерства образования РФ (Челябинское отделение) в качестве учебного пособия для студентов, магистрантов и аспирантов математических специальностей университетов.
М.: Мир, 1974, - 200 с. Автор книги хорошо знаком читателю. В переводе на русский язык уже выходили его книги «Теория Морса» («Мир», 1965), «Теорема об h-кобордизме» («Мир», 1969), «Особые точки комплексных гиперповерхностей» («Мир», 1971) и др. Он зарекомендовал себя не только как крупный ученый, но и как мастер исключительно наглядного и ясного изложения новых идей в...
Современные проблемы математики/ Математический институт имени В. А. Стеклова РАН (МИАН). - М.: МИАН, 2004. Вып.
4. - 46 с.
Серия "Современные проблемы математики" - рецензируемое продолжающееся издание МИАН. В серии публикуются работы, отражающие достижения сотрудников и аспирантов МИАН. Особое внимание уделяется исследованиям, выполняемым в рамках программ РАН.
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М.: «Мир», 1968.
Книга написана на основе лекций, прочитанных видным французским математиком. С присущим автору мастерством в этих лекциях изложены основы теории когомологий топологических вполне несвязных групп и их многочисленные приложения к теории чисел и алгебраической геометрии, концентрирующиеся вокруг понятий когомологической размерности поля, диофантовых проблем в теории...
М.: Московский физико-технический институт, Независимый московский университет, 2014. — 171 с. Алгебраическая топология является фундаментальной частью математики и имеет применения за ее пределами. Как и для любой фундаментальной части науки, ее основные мотивировки и идеи можно доступно изложить человеку, не имеющему глубоких специальных познаний. Такому изложению посвящена...
Учебное пособие. — М.: Московский государственный университет (МГУ) имени М.В. Ломоносова, 2023. — 161 с. Основная идея этой книги — показать, как алгебраические идеи возникают и работают при решении топологических задач. Основное ее содержание — алгоритмически мотивированное введение в алгебраическую топологию (точнее, в теорию гомологий и в теорию препятствий). Дается...
Электронное издание. — М.: МЦНМО, 2016. — 269 с. — ISBN: 9785443924779. В книге рассматриваются важнейшие наглядные объекты математики, важные для приложений: маломерные многообразия и векторные поля на них, непрерывные отображения и их деформации. Показано, как при решении геометрических проблем естественно возникают основные идеи, понятия и методы алгебраической топологии:...
Учебное пособие. - Москва, 2005. — 128 с., Учебное пособие, eBook, Русский. Чтение этой брошюры и решение задач потребуют от читателя усилий, однако эти усилия будут сполна оправданы тем, что вслед за великими математиками 20-го века в процессе изучения геометрических проблем читатель откроет некоторые основные понятия и теоремы алгебраической топологии. Надеюсь, это поможет...
М.: Мир, 1982. — 280 с. Книга канадского математика, содержащая результаты, открывающие новые связи алгебраической топологии с алгебраической геометрией, алгеброй и теорией чисел. В ней с единых позиций представлены современные достижения алгебраической топологии.
Книга известного американского математика, содержащая весьма полное и последовательное изложение идей, методов и результатов современной алгебраической топологии, включая теорию гомотопий, гомологии, теорию препятствий и т. д. После каждой главы приводятся упражнения, удачно дополняющие основной текст. От читателя не требуется почти никаких предварительных знаний в этой области....
МИР 1971 стр.680 Книга известного американского математика, содержащая весьма полное и последлвательное изложение идей, методов и результатов современной алгебраической топологии, включая теорию гомотопий, гомологии, теорию препятствий и т.д.
М.: Мир, 1971. - 693 с.
Книга известного американского математика, содержащая весьма полное и последовательное изложение идей, методов и результатов современной алгебраической топологии, включая теорию гомотопий, гомологии, теорию препятствий и т.д. После каждой главы приводятся упражнения, удачно дополняющие основной текст. От читателя не требуется почти никаких предварительных...
Перевод с английского Б.С. Виленской. — Под редакцией М.М. Постникова. — М.: Государственное издательство физико-математической литературы (ГИФМЛ), 1958. — 403 с. Настоящая книга содержит аксиоматическое изложение теории гомологий, наиболее развитой ветви алгебраической топологии. В связи с таким построением теория гомологий приобретает более доступный вид. Преимущества чисто...
Перевод с английского В.М. Бухштабера, М.: Мир, 1973, - 372 с. Единственный пока в мировой математической литературе учебник по новому, очень перспективному разделу алгебраической топологии. Первая его часть наряду с построением теорий кобордизмов содержит хорошее введение в общую теорию характеристических классов; во второй части дано систематическое изложение результатов и...
Перевод с английского В.М. Бухштабера. — М.: Мир, 1973. — 372 с. Единственный пока в мировой математической литературе учебник по новому, очень перспективному разделу алгебраической топологии. Первая его часть наряду с построением теорий кобордизмов содержит хорошее введение в общую теорию характеристических классов; во второй части дано систематическое изложение результатов и...
Москва: МЦНМО, 2004. — 136 с. — ISBN: 5-94057-129-8 Книга представляет собой введение в комбинаторные кручения клеточных пространств и многообразий. Особенно подробно рассматриваются кручения трехмерных многообразий. Две первые главы охватывают алгебраические основы теории кручений и разнообразные топологические конструкции кручений. Также обсуждается связь между кручениями и...
М.: МЦНМО, 2011. — 688 с. — ISBN: 978-5-94057-748-5. Переводчик: В.В.Прасолов под ред. Т.Е.Панова. Книга представляет собой введение в алгебраическую топологию (до спектральных последовательностей), включающее в себя как гомотопическую топологию, так и теорию гомологий и когомологий (в том числе двойственность Пуанкаре). Ориентированное на геометрические аспекты предмета...
Перевод с англ. В.В. Прасолова. — Под ред. Т.Е. Панова. — М.: Московский центр непрерывного математического образования (МЦНМО), 2011. — 688 с. — ISBN 978-5-94057-748-5. Книга представляет собой введение в алгебраическую топологию (до спектральных последовательностей), включающее в себя как гомотопическую топологию, так и теорию гомологий и когомологий (в том числе...
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