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Progress in Mathematics #174: Simplicial Homotopy Theory

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Progress in Mathematics #174: Simplicial Homotopy Theory Cover

 

Synopses & Reviews

Publisher Comments:

Since the beginning of the modern era of algebraic topology, simplicialmethods 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 basictopics 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 aremany results and ideas well-known to experts, but uncollected in theliterature.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.

Product Details

ISBN:
9783764360641
Other:
Goerss, Paul Gregory
Author:
Jardine, John F.
Author:
Goerss, Paul Gregory
Author:
Goerss, P. G.
Author:
Goerss, Paul G.
Author:
Jardine, J. F.
Publisher:
Birkhauser
Subject:
Topology
Subject:
Algebraic topology
Subject:
Homotopy theory
Subject:
Topology - General
Subject:
General Mathematics
Subject:
Algebraic K-theory
Subject:
MATHEMATICS / Topology
Copyright:
Edition Number:
1
Series:
Progress in Mathematics
Series Volume:
174
Publication Date:
September 1999
Binding:
Hardcover
Language:
English
Pages:
500
Dimensions:
9.42x6.41x1.24 in. 2.20 lbs.

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Related Subjects


Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Topology

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