Simplicial Homotopy Theory (Progress in Mathematics) - Softcover
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.
"synopsis" may belong to another edition of this title.
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"... 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
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- PublisherBirkhäuser
- Publication date2012
- ISBN 10 3034897375
- ISBN 13 9783034897372
- BindingPaperback
- Number of pages525
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Book Description Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 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 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 well-known to experts, but uncollected in theliterature.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. 510 pp. Englisch. Seller Inventory # 9783034897372
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Book Description Kartoniert / Broschiert. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. I Simplicial sets.- 1. Basic definitions.- 2. Realization.- 3. Kan complexes.- 4. Anodyne extensions.- 5. Function complexes.- 6. Simplicial homotopy.- 7. Simplicial homotopy groups.- 8. Fundamental groupoid.- 9. Categories of fibrant objects.- 10. Minimal . Seller Inventory # 4319549
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Book Description Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 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 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 well-known to experts, but uncollected in theliterature.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. Seller Inventory # 9783034897372
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