Introduction To Homotopy Theory

Author : Martin Arkowitz
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 46,6 Mb
Release : 2011-07-25
Category : Mathematics
ISBN : 9781441973290

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Introduction to Homotopy Theory by Martin Arkowitz Pdf

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.

Author : Paul Selick
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 41,6 Mb
Release : 2008
Category : Mathematics
ISBN : 0821844369

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Introduction to Homotopy Theory by Paul Selick Pdf

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.

Author : Jeffrey Strom
Publisher : American Mathematical Society
Page : 862 pages
File Size : 46,9 Mb
Release : 2023-01-19
Category : Mathematics
ISBN : 9781470471637

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Modern Classical Homotopy Theory by Jeffrey Strom Pdf

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.

Author : Anonim
Publisher : Academic Press
Page : 367 pages
File Size : 48,8 Mb
Release : 1975-11-12
Category : Mathematics
ISBN : 0080873804

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Homotopy Theory: An Introduction to Algebraic Topology by Anonim Pdf

Homotopy Theory: An Introduction to Algebraic Topology

Author : P. J. Hilton
Publisher : Unknown
Page : 142 pages
File Size : 42,8 Mb
Release : 1953-01-01
Category : Mathematics
ISBN : 0521052653

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An Introduction to Homotopy Theory by P. J. Hilton Pdf

Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has occupied a prominent place in the development of algebraic topology. This monograph provides an account of the subject which bridges the gap between the fundamental concepts of topology and the more complex treatment to be found in original papers. The first six chapters describe the essential ideas of homotopy theory: homotopy groups, the classical theorems, the exact homotopy sequence, fibre-spaces, the Hopf invariant, and the Freudenthal suspension. The final chapters discuss J. H. C. Whitehead's cell-complexes and their application to homotopy groups of complexes.

Author : Anonim
Publisher : Univalent Foundations
Page : 484 pages
File Size : 40,8 Mb
Release : 2024-06-02
Category : Electronic
ISBN : 8210379456XXX

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Homotopy Type Theory: Univalent Foundations of Mathematics by Anonim Pdf

Author : Birgit Richter
Publisher : Cambridge University Press
Page : 401 pages
File Size : 54,8 Mb
Release : 2020-04-16
Category : Mathematics
ISBN : 9781108479622

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From Categories to Homotopy Theory by Birgit Richter Pdf

Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.

Author : Anonim
Publisher : Academic Press
Page : 346 pages
File Size : 41,9 Mb
Release : 1959-01-01
Category : Mathematics
ISBN : 0080873162

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Homotopy Theory by Anonim Pdf

Homotopy Theory

Author : Emily Riehl
Publisher : Cambridge University Press
Page : 371 pages
File Size : 55,7 Mb
Release : 2014-05-26
Category : Mathematics
ISBN : 9781107048454

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Categorical Homotopy Theory by Emily Riehl Pdf

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.

Author : George W. Whitehead
Publisher : Springer Science & Business Media
Page : 764 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461263180

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Elements of Homotopy Theory by George W. Whitehead Pdf

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.

Author : Haynes Miller
Publisher : CRC Press
Page : 1043 pages
File Size : 46,9 Mb
Release : 2020-01-23
Category : Mathematics
ISBN : 9781351251600

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Handbook of Homotopy Theory by Haynes Miller Pdf

The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Author : Anonim
Publisher : Unknown
Page : 142 pages
File Size : 47,5 Mb
Release : 1952
Category : Electronic
ISBN : OCLC:867454025

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An Introduction to Homotopy Theory by Anonim Pdf

Author : M.M. Cohen
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493726

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A Course in Simple-Homotopy Theory by M.M. Cohen Pdf

This book grew out of courses which I taught at Cornell University and the University of Warwick during 1969 and 1970. I wrote it because of a strong belief that there should be readily available a semi-historical and geo metrically motivated exposition of J. H. C. Whitehead's beautiful theory of simple-homotopy types; that the best way to understand this theory is to know how and why it was built. This belief is buttressed by the fact that the major uses of, and advances in, the theory in recent times-for example, the s-cobordism theorem (discussed in §25), the use of the theory in surgery, its extension to non-compact complexes (discussed at the end of §6) and the proof of topological invariance (given in the Appendix)-have come from just such an understanding. A second reason for writing the book is pedagogical. This is an excellent subject for a topology student to "grow up" on. The interplay between geometry and algebra in topology, each enriching the other, is beautifully illustrated in simple-homotopy theory. The subject is accessible (as in the courses mentioned at the outset) to students who have had a good one semester course in algebraic topology. I have tried to write proofs which meet the needs of such students. (When a proof was omitted and left as an exercise, it was done with the welfare of the student in mind. He should do such exercises zealously.

Author : Paul G. Goerss,John F. Jardine
Publisher : Birkhäuser
Page : 520 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887076

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Simplicial Homotopy Theory by Paul G. Goerss,John F. Jardine Pdf

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.

Author : David Barnes,Constanze Roitzheim
Publisher : Cambridge University Press
Page : 432 pages
File Size : 51,5 Mb
Release : 2020-03-26
Category : Mathematics
ISBN : 9781108672672

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Foundations of Stable Homotopy Theory by David Barnes,Constanze Roitzheim Pdf

The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. The appendix containing essential facts on model categories, the numerous examples and the suggestions for further reading make this a friendly introduction to an often daunting subject.