Modern Birkhäuser Classics

Simplicial Homotopy Theory

Authors: Goerss, Paul G., Jardine, John

  • Introduces many of the basic tools of modern homotopy theory.
  • Coverage does not assume an extensive background in topology
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eBook $69.99
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  • ISBN 978-3-0346-0189-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-0346-0188-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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

Reviews

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


Table of contents (10 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0346-0189-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-0346-0188-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Simplicial Homotopy Theory
Authors
Series Title
Modern Birkhäuser Classics
Copyright
2009
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-0346-0189-4
DOI
10.1007/978-3-0346-0189-4
Softcover ISBN
978-3-0346-0188-7
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XVI, 510
Topics