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 nonabelian homological algebra and to address homotopytheoretical issues in a variety of fields, including algebraic Ktheory. 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 wellknown to experts, but uncollected in theliterature. Intended for secondyear graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.

Authors: Goerss P.G., Jardine J.F.  Pages: 546 Year: 1997 
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