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Author Goerss, Paul G. author Simplicial Homotopy Theory [electronic resource] / by Paul G. Goerss, John F. Jardine Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1999 http://dx.doi.org/10.1007/978-3-0348-8707-6 XV, 510 p. online resource

CONTENT

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. Quillenโ{128}{153}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, Milnorโ{128}{153}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 homotopy spectral 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

Mathematics Topology Algebraic topology Mathematics Algebraic Topology Topology

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