Homotopy Theory
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Introduction To Homotopy Theory
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Author : Martin Arkowitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-25
Introduction To Homotopy Theory written by Martin Arkowitz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-25 with Mathematics categories.
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.
Primary Homotopy Theory
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Author : Joseph Neisendorfer
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
Primary Homotopy Theory written by Joseph Neisendorfer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
The author gives a systematic exposition of homotopy groups with coefficients in a cyclic group [italic]Z or [italic]Z[subscript italic]k. The text pays particular attention to low-dimensional cases and trouble with the small primes. The book gives a complete treatment of some topics--such as Samelson products--with a view toward applications.
From Categories To Homotopy Theory
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Author : Birgit Richter
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-16
From Categories To Homotopy Theory written by Birgit Richter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-16 with Mathematics categories.
Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.
Homotopy Theory
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Author :
language : en
Publisher: Academic Press
Release Date : 1959-01-01
Homotopy Theory written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959-01-01 with Mathematics categories.
Homotopy Theory
Rational Homotopy Theory
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Author : Yves Felix
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Rational Homotopy Theory written by Yves Felix and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Rational homotopy theory is a subfield of algebraic topology. Written by three authorities in the field, this book contains all the main theorems of the field with complete proofs. As both notation and techniques of rational homotopy theory have been considerably simplified, the book presents modern elementary proofs for many results that were proven ten or fifteen years ago.
Categorical Homotopy Theory
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Author : Emily Riehl
language : en
Publisher: Cambridge University Press
Release Date : 2014-05-26
Categorical Homotopy Theory written by Emily Riehl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-26 with Mathematics categories.
This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.
Elements Of Homotopy Theory
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Author : George W. Whitehead
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Elements Of Homotopy Theory written by George W. Whitehead and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Simplicial Homotopy Theory
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Author : Paul G. Goerss
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Simplicial Homotopy Theory written by Paul G. Goerss and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.
Homotopy Theory An Introduction To Algebraic Topology
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Author :
language : en
Publisher: Academic Press
Release Date : 1975-11-12
Homotopy Theory An Introduction To Algebraic Topology written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-11-12 with Mathematics categories.
Homotopy Theory: An Introduction to Algebraic Topology
Introduction To Homotopy Theory
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Author : Paul Selick
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Introduction To Homotopy Theory written by Paul Selick and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.