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Simplicial Objects in Algebraic Topology

by Peter May

  • ISBN: 9780226511818
  • ISBN10: 0226511812

Simplicial Objects in Algebraic Topology

by Peter May

  • Binding: Paperback
  • Publisher: Univ of Chicago Pr
  • Publish date: 01/01/1993
  • ISBN: 9780226511818
  • ISBN10: 0226511812
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Description: I. SIMPLICIAL OBJECTS AND HOMOTOPY 1. Definitions and examples 2. Simplicial objects in categories; homology3. Homotopy of Kan complexes 4. The group structures5. Homotopy of simplicial maps 6. Function complexes Bibliographical notes on chapter I II. FIBRATIONS, POSTNIKOV SYSTEMS, AND MINIMAL COMPLEXES 7. Kan fibrations 8. Postnikov systems9. Minimal complexes10. Minimal fibrations 11. Fibre products and fibre bundles 12. Weak homotopy type 13. The Hurewicz theoremsBibliographical notes on chapter II III. GEOMETRIC REALIZATION 14. The realization 15. Adjoint functors 16. Comparison of simplicial sets and topological spacesBibliographical notes on chapter IIIIV. TWISTED CARTESIAN PRODUCTS AND FIBRE BUNDLES17. Simplicial groups18. Principal fibrations and twisted Cartesian products19. The group of a fibre bundle20. Fibre bundles and twisted Cartesian products 21. Universal bundles and classifying complexes Bibliographical notes on chapter IV V. EILENBERG-MACLANE COMPLEXES AND POSTNIKOV SYSTEMS 22. Simplicial Abelian groups 23. Eilenberg-MacLane complexes 24. K(rr, n)'s and cohomology operations 25. The k-invariants of Postnikov systems Bibliographical notes on chapter V VI. LOOP GROUPS, ACYCLIC MODELS, AND TWISTED TENSOR PRODUCTS26. Loop groups 27. The functors G, W, and E 28. Acyclic models29. The Eilenberg-Zilber theorem30. Cup, Pontryagin, and cap products; twisting cochains31. Brown's theorem 32. The Serre spectral sequence Bibliographical notes on chapter VI BIBLIOGRAPHY
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