Simplicial Homotopy Theory (Progress in Mathematics) by Paul G. Goerss

Simplicial Homotopy Theory (Progress in Mathematics) by Paul G. Goerss

Publisher: Birkhäuser Basel; 1 edition (September 24, 1999) | ISBN: 376436064X | Pages: 510 | DJVU | 2.68 MB

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.