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Simplicial Homotopy Theory

Bibliographic Details
Main Authors: Goerss, Paul G., Jardine, John F. (Author)
Format: eBook
Language:English
Published: Basel Birkhäuser 1999, 1999
Edition:1st ed. 1999
Series:Progress in Mathematics
Subjects:
Algebraic Topology
Topology
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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

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