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＜電子ブック＞
Simplicial Homotopy Theory / by Paul G. Goerss, John F. Jardine
(Progress in Mathematics. ISSN:2296505X ; 174)

版	1st ed. 1999.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	1999
本文言語	英語
大きさ	XV, 510 p : online resource
著者標目	*Goerss, Paul G author Jardine, John F author SpringerLink (Online service)
件　名	LCSH:Algebraic topology LCSH:Topology FREE:Algebraic Topology FREE:Topology
一般注記	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 fibrations -- 11. The closed model structure -- II Model Categories -- 1. Homotopical algebra -- 2. Simplicial categories -- 3. Simplicial model categories -- 4. The existence of simplicial model category structures -- 5. Examples of simplicial model categories -- 6. A generalization of Theorem 4.1 -- 7. Quillen’s total derived functor theorem -- 8. Homotopy cartesian diagrams -- III Classical results and constructions -- 1. The fundamental groupoid, revisited -- 2. Simplicial abelian groups -- 3. The Hurewicz map -- 4. The Ex? functor -- 5. The Kan suspension -- IV Bisimplicial sets -- 1. Bisimplicial sets: first properties -- 2. Bisimplicial abelian groups -- 3. Closed model structures for bisimplicial sets -- 4. The Bousfield-Friedlander theorem -- 5. Theorem B and group completion -- V Simplicial groups -- 1. Skeleta -- 2. Principal fibrations I: simplicial G-spaces -- 3. Principal fibrations II: classifications -- 4. Universal cocycles and $$ \bar W $$G -- 5. The loop group construction -- 6. Reduced simplicial sets, Milnor’s FK-construction -- 7. Simplicial groupoids -- VI The homotopy theory of towers -- 1. A model category structure for towers of spaces -- 2. The spectral sequence of a tower of fibrations -- 3. Postnikov towers -- 4. Local coefficients and equivariant cohomology -- 5. On k-invariants -- 6. Nilpotent spaces -- VII Reedy model categories -- 1. Decomposition of simplicial objects -- 2. Reedy model category structures -- 3. Geometric realization -- 4. Cosimplicial spaces -- VIII Cosimplicial spaces: applications -- 1. The homotopyspectral sequence of a cosimplicial space -- 2. Homotopy inverse limits -- 3. Completions -- 4. Obstruction theory -- IX Simplicial functors and homotopy coherence -- 1. Simplicial functors -- 2. The Dwyer-Kan theorem -- 3. Homotopy coherence -- 4. Realization theorems -- X Localization -- 1. Localization with respect to a map -- 2. The closed model category structure -- 3. Bousfield localization -- 4. A model for the stable homotopy category -- References HTTP:URL=https://doi.org/10.1007/978-3-0348-8707-6

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