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.
General
Imprint: |
Birkhauser Verlag AG
|
Country of origin: |
Switzerland |
Series: |
Progress in Mathematics, 174 |
Release date: |
October 2012 |
First published: |
October 2012 |
Authors: |
Paul G. Goerss
• John F. Jardine
|
Dimensions: |
235 x 155 x 32mm (L x W x T) |
Format: |
Paperback
|
Pages: |
510 |
Edition: |
Softcover reprint of the original 1st ed. 1999 |
ISBN-13: |
978-3-03-489737-2 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Topology >
Algebraic topology
|
LSN: |
3-03-489737-5 |
Barcode: |
9783034897372 |
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