Format:
Online-Ressource
,
v.: digital
Edition:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
1282827243
,
9781282827240
,
9783034601887
Series Statement:
Modern Birkhäuser Classics
Content:
" 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. Reviews: ""... a book filling an obvious gap in the literature and the authors have done an excellent job on it. No monograph or expository paper has been published on this topic in the last twenty-eight years."" - Analele Universitatii din Timisoara ""... is clearly presented and a brief summary preceding every chapter is useful to the reader. The book should prove enlightening to a broad range of readers including prospective students and researchers who want to apply simplicial techniques for whatever reason."" - Zentralblatt MATH ""... they succeed. The book is an excellent account of simplicial homotopy theory from a modern point of view [...] The book is well written. [...] The book can be highly recommended to anybody who wants to learn and to apply simplicial techniques and/or the theory of (simplicial) closed model categories."" - Mathematical Reviews"
Note:
"Reprint of the 1999 edition
,
Includes bibliographical references and index
,
CONTENTS; Chapter I Simplicial sets; Chapter II Model Categories; Chapter III Classical results and constructions; Chapter IV Bisimplicial sets; Chapter V Simplicial groups; Chapter VI The homotopy theory of towers; Chapter VII Reedy model categories; Chapter VIII Cosimplicial spaces: applications; Chapter IX Simplicial functors and homotopy coherence; Chapter X Localization; References; Index;
,
Electronic reproduction; Available via World Wide Web
Additional Edition:
ISBN 9783034601894
Additional Edition:
ISBN 9783034601887
Additional Edition:
Erscheint auch als Druck-Ausgabe Goerss, Paul G. Simplicial homotopy theory Basel : Birkhäuser, 2009 ISBN 9783034601887
Language:
English
Subjects:
Mathematics
Keywords:
Homotopietheorie
;
Simplex
DOI:
10.1007/978-3-0346-0189-4
URL:
Volltext
(lizenzpflichtig)
Author information:
Goerss, Paul G.
Author information:
Jardine, John F. 1951-
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