Simplicial Homotopy Theory

  • Paul G. Goerss
  • John F. Jardine

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Paul G. Goerss, John F. Jardine
    Pages 1-64
  3. Paul G. Goerss, John F. Jardine
    Pages 65-138
  4. Paul G. Goerss, John F. Jardine
    Pages 139-194
  5. Paul G. Goerss, John F. Jardine
    Pages 195-249
  6. Paul G. Goerss, John F. Jardine
    Pages 251-305
  7. Paul G. Goerss, John F. Jardine
    Pages 307-351
  8. Paul G. Goerss, John F. Jardine
    Pages 353-387
  9. Paul G. Goerss, John F. Jardine
    Pages 389-429
  10. Paul G. Goerss, John F. Jardine
    Pages 431-462
  11. Paul G. Goerss, John F. Jardine
    Pages 463-502
  12. Back Matter
    Pages 503-510

About this book

Introduction

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

Keywords

Algebraic topology Homotopy K-theory algebraic K-theory homological algebra homology homotopy theory

Authors and affiliations

  • Paul G. Goerss
    • 1
  • John F. Jardine
    • 2
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA
  2. 2.Department of MathematicsThe University of Western OntarioLondonCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0346-0189-4
  • Copyright Information Birkhäuser Basel 2009
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0346-0188-7
  • Online ISBN 978-3-0346-0189-4
  • About this book