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Author :
Publisher : Univalent Foundations
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4./5 ( download)
Download or read book Homotopy Type Theory: Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Martin Arkowitz
Publisher : Springer Science & Business Media
ISBN 13 : 144197329X
Total Pages : 352 pages
Book Rating : 4.4/5 (419 download)
Download or read book Introduction to Homotopy Theory written by Martin Arkowitz and published by Springer Science & Business Media. This book was released on 2011-07-25 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : George W. Whitehead
Publisher : Springer Science & Business Media
ISBN 13 : 1461263182
Total Pages : 764 pages
Book Rating : 4.4/5 (612 download)
Download or read book Elements of Homotopy Theory written by George W. Whitehead and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jeffrey Strom
Publisher : American Mathematical Society
ISBN 13 : 1470471639
Total Pages : 862 pages
Book Rating : 4.4/5 (74 download)
Download or read book Modern Classical Homotopy Theory written by Jeffrey Strom and published by American Mathematical Society. This book was released on 2023-01-19 with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Emily Riehl
Publisher : Cambridge University Press
ISBN 13 : 1139952633
Total Pages : 371 pages
Book Rating : 4.1/5 (399 download)
Download or read book Categorical Homotopy Theory written by Emily Riehl and published by Cambridge University Press. This book was released on 2014-05-26 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
Author : Ioan James
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.3/5 (91 download)
Download or read book On Homotopy written by Ioan James and published by . This book was released on 1960 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yves Felix
Publisher : Springer Science & Business Media
ISBN 13 : 146130105X
Total Pages : 574 pages
Book Rating : 4.4/5 (613 download)
Download or read book Rational Homotopy Theory written by Yves Felix and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : James D. Stasheff
Publisher :
ISBN 13 :
Total Pages : 58 pages
Book Rating : 4.3/5 (91 download)
Download or read book On Homotopy Abelian H-spaces written by James D. Stasheff and published by . This book was released on 1961 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mila Cenkl
Publisher : American Mathematical Soc.
ISBN 13 : 0821802968
Total Pages : 422 pages
Book Rating : 4.8/5 (218 download)
Download or read book The ?ech Centennial written by Mila Cenkl and published by American Mathematical Soc.. This book was released on 1995 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the refereed proceedings of the %Cech Centennial Homotopy Theory Conference, organized to commemorate the 100th anniversary of the birth of Eduard %Cech and held at Northeastern University in June 1993. Focusing on the theme of stable and unstable homotopy theory, the conference attracted more than one hundred mathematicians from around the world. With recent results by some of the leaders in the field, this book will provide readers with a look at important directions in current research in homotopy theory.
Author : John Frank Adams
Publisher : University of Chicago Press
ISBN 13 : 0226005240
Total Pages : 384 pages
Book Rating : 4.2/5 (26 download)
Download or read book Stable Homotopy and Generalised Homology written by John Frank Adams and published by University of Chicago Press. This book was released on 1974 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Author : Robert M. Switzer
Publisher : Springer
ISBN 13 : 3642619231
Total Pages : 541 pages
Book Rating : 4.6/5 (426 download)
Download or read book Algebraic Topology - Homotopy and Homology written by Robert M. Switzer and published by Springer. This book was released on 2017-12-01 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Douglas C. Ravenel
Publisher : American Mathematical Society
ISBN 13 : 1470472937
Total Pages : 417 pages
Book Rating : 4.4/5 (74 download)
Download or read book Complex Cobordism and Stable Homotopy Groups of Spheres written by Douglas C. Ravenel and published by American Mathematical Society. This book was released on 2023-02-09 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.
Author : Paul G. Goerss
Publisher : Birkhäuser
ISBN 13 : 3034887078
Total Pages : 520 pages
Book Rating : 4.0/5 (348 download)
Download or read book Simplicial Homotopy Theory written by Paul G. Goerss and published by Birkhäuser. This book was released on 2012-12-06 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : M.M. Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 1468493728
Total Pages : 124 pages
Book Rating : 4.4/5 (684 download)
Download or read book A Course in Simple-Homotopy Theory written by M.M. Cohen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Birgit Richter
Publisher : Cambridge University Press
ISBN 13 : 1108847625
Total Pages : 402 pages
Book Rating : 4.1/5 (88 download)
Download or read book From Categories to Homotopy Theory written by Birgit Richter and published by Cambridge University Press. This book was released on 2020-04-16 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
Author : Julia E. Bergner
Publisher : Cambridge University Press
ISBN 13 : 1108565042
Total Pages : 290 pages
Book Rating : 4.1/5 (85 download)
Download or read book The Homotopy Theory of (∞,1)-Categories written by Julia E. Bergner and published by Cambridge University Press. This book was released on 2018-03-15 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of an (∞,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many different approaches to this structure, all of them equivalent, and each with its corresponding homotopy theory. This book provides a relatively self-contained source of the definitions of the different models, the model structure (homotopy theory) of each, and the equivalences between the models. While most of the current literature focusses on how to extend category theory in this context, and centers in particular on the quasi-category model, this book offers a balanced treatment of the appropriate model structures for simplicial categories, Segal categories, complete Segal spaces, quasi-categories, and relative categories, all from a homotopy-theoretic perspective. Introductory chapters provide background in both homotopy and category theory and contain many references to the literature, thus making the book accessible to graduates and to researchers in related areas.
Author : James Stasheff
Publisher : Springer
ISBN 13 : 3540363149
Total Pages : 100 pages
Book Rating : 4.5/5 (43 download)
Download or read book H-Spaces from a Homotopy Point of View written by James Stasheff and published by Springer. This book was released on 2006-11-15 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
