Simplicial Objects in Algebraic Topology
Paper $22.00
ISBN: 9780226511818
Published January 1993
I. SIMPLICIAL OBJECTS AND HOMOTOPY 1. Definitions and examples 2. Simplicial objects in categories; homology 3. Homotopy of Kan complexes 4. The group structures 5. Homotopy of simplicial maps 6. Function complexes Bibliographical notes on chapter I II. FIBRATIONS, POSTNIKOV SYSTEMS, AND MINIMAL COMPLEXES 7. Kan fibrations 8. Postnikov systems 9. Minimal complexes 10. Minimal fibrations 11. Fibre products and fibre bundles 12. Weak homotopy type 13. The Hurewicz theorems Bibliographical notes on chapter II III. GEOMETRIC REALIZATION 14. The realization 15. Adjoint functors 16. Comparison of simplicial sets and topological spaces Bibliographical notes on chapter III IV. TWISTED CARTESIAN PRODUCTS AND FIBRE BUNDLES 17. Simplicial groups 18. Principal fibrations and twisted Cartesian products 19. The group of a fibre bundle 20. 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 PRODUCTS 26. Loop groups 27. The functors G, W, and E 28. Acyclic models 29. The Eilenberg-Zilber theorem 30. Cup, Pontryagin, and cap products; twisting cochains 31. Brown's theorem 32. The Serre spectral sequence Bibliographical notes on chapter VI BIBLIOGRAPHY
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