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Simplicial Homotopy Theory

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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Series Title
Modern Birkhäuser Classics
Call Number
510
Publisher
Basel : Birkhäuser Basel.,
Collation
Mathematics
Language
English
ISBN/ISSN
978-3-0346-0189-4
Classification
NONE
Content Type
text
Media Type
computer
Carrier Type
online resource
Edition
1
Subject(s)
Mathematics
general
Mathematics general
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Cataloger
Suwardi
Source
https://link.springer.com/book/10.1007/978-3-0346-0189-4
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