Item description for Simplicial Homotopy Theory (Progress in Mathematics) by Paul Gregory Goerss & J. F. Jardine...
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.
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Est. Packaging Dimensions: Length: 1.25" Width: 6.5" Height: 9.75" Weight: 2.25 lbs.
Release Date Sep 24, 1999
Publisher Birkhäuser Basel
ISBN 376436064X ISBN13 9783764360641
Reviews - What do customers think about Simplicial Homotopy Theory (Progress in Mathematics)?
Excellent book! Jun 19, 2001
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.