Author: Publisher: Academic Press
ISBN: 9780080873800
Category : Mathematics
Languages : en
Pages : 367
Book Description
Homotopy Theory: An Introduction to Algebraic Topology
Homotopy Theory: An Introduction to Algebraic Topology
Author: Publisher: Academic Press
ISBN: 9780080873800
Category : Mathematics
Languages : en
Pages : 367
Book Description
Homotopy Theory: An Introduction to Algebraic Topology
Homology Theory
Author: James W. VickPublisher: Springer Science & Business Media
ISBN: 1461208815
Category : Mathematics
Languages : en
Pages : 258
Book Description
This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.
Introduction to Homotopy Theory
Author: Martin ArkowitzPublisher: Springer Science & Business Media
ISBN: 144197329X
Category : Mathematics
Languages : en
Pages : 352
Book Description
This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: Basic Homotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotopy sets, actions, and coactions; homotopy pushouts and pullbacks; classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; homotopy Sets; homotopy and homology decompositions of spaces and maps; and obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory. The book can be used as a text for the second semester of an advanced ungraduate or graduate algebraic topology course.
Algebraic Topology - Homotopy and Homology
Author: Robert M. SwitzerPublisher: Springer
ISBN: 3642619231
Category : Mathematics
Languages : en
Pages : 541
Book Description
From the reviews: "The author has attempted an ambitious and most commendable project. [...] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. [...] This book is, all in all, a very admirable work and a valuable addition to the literature." Mathematical Reviews
Introduction to Homotopy Theory
Author: Paul SelickPublisher: American Mathematical Soc.
ISBN: 9780821844366
Category : Mathematics
Languages : en
Pages : 220
Book Description
Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.
Modern Classical Homotopy Theory
Author: Jeffrey StromPublisher: American Mathematical Society
ISBN: 1470471639
Category : Mathematics
Languages : en
Pages : 862
Book Description
The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.
Algebraic Topology
Author: C. R. F. MaunderPublisher: Courier Corporation
ISBN: 9780486691312
Category : Mathematics
Languages : en
Pages : 414
Book Description
Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.
Elements of Homotopy Theory
Author: George W. WhiteheadPublisher: Springer Science & Business Media
ISBN: 1461263182
Category : Mathematics
Languages : en
Pages : 764
Book Description
As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory. It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal Coefficient and Kiinneth Theorems. Some acquaintance with manifolds and Poincare duality is desirable, but not essential. Anyone who has taught a course in algebraic topology is familiar with the fact that a formidable amount of technical machinery must be introduced and mastered before the simplest applications can be made. This phenomenon is also observable in the more advanced parts of the subject. I have attempted to short-circuit it by making maximal use of elementary methods. This approach entails a leisurely exposition in which brevity and perhaps elegance are sacrificed in favor of concreteness and ease of application. It is my hope that this approach will make homotopy theory accessible to workers in a wide range of other subjects-subjects in which its impact is beginning to be felt. It is a consequence of this approach that the order of development is to a certain extent historical. Indeed, if the order in which the results presented here does not strictly correspond to that in which they were discovered, it nevertheless does correspond to an order in which they might have been discovered had those of us who were working in the area been a little more perspicacious.
Homotopy Type Theory: Univalent Foundations of Mathematics
Author: Publisher: Univalent Foundations
ISBN:
Category :
Languages : en
Pages : 484
Book Description
Algebraic Topology
Author: Allen HatcherPublisher: Cambridge University Press
ISBN: 9780521795401
Category : Mathematics
Languages : en
Pages : 572
Book Description
An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.