Simplicial Homotopy Theory (Modern Birkhäuser Classics) 2010th Edition by Paul G. Goerss (PDF)

Description

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.Reviews:”… a book filling an obvious gap in the literature and the authors have done an excellent job on it. No monograph or expository paper has been published on this topic in the last twenty-eight years.” – Analele Universitatii din Timisoara”… is clearly presented and a brief summary preceding every chapter is useful to the reader. The book should prove enlightening to a broad range of readers including prospective students and researchers who want to apply simplicial techniques for whatever reason.” – Zentralblatt MATH “… they succeed. The book is an excellent account of simplicial homotopy theory from a modern point of view […] The book is well written. […] The book can be highly recommended to anybody who wants to learn and to apply simplicial techniques and/or the theory of (simplicial) closed model categories.” – Mathematical Reviews

User’s Reviews

Editorial Reviews: Review From reviews:”… a book filling an obvious gap in the literature and the authors have done an excellent job on it. No monograph or expository paper has been published on this topic in the last twenty-eight years.” – Analele Universitatii din Timisoara”… is clearly presented and a brief summary preceding every chapter is useful to the reader. The book should prove enlightening to a broad range of readers including prospective students and researchers who want to apply simplicial techniques for whatever reason.” – Zentralblatt MATH “… they succeed. The book is an excellent account of simplicial homotopy theory from a modern point of view […] The book is well written. […] The book can be highly recommended to anybody who wants to learn and to apply simplicial techniques and/or the theory of (simplicial) closed model categories.” – Mathematical Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐i still can’t figure out how you can explain why someone is gay using the math in this book. admittedly i have problems understanding long division so about the only thing that made sense to me in this book where the page numbers. which run in sequential order thank god.

⭐Gives a well-written and concise treatment of developments in an area of topology that has seen considerable progress in the past 50 years. The only other general expository books in this area are more than 20 years old. This is particularly important because the book unifies many seemingly disparate results and approaches. Even classic constructions (like the Hurewicz homomorphism) are give modern (and very concise) interpretations. I strongly recommend this book to students and researchers in algebraic topology.

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Simplicial Homotopy Theory (Modern Birkhäuser Classics) 2010th Edition 2010 PDF Free Download
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