Simplicial Objects in Algebraic Topology
170 pages

51\2 x 81\2

© 1967
Contents
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. EILENBERGMACLANE COMPLEXES AND POSTNIKOV SYSTEMS
22. Simplicial Abelian groups
23. EilenbergMacLane complexes
24. K(rr, n)'s and cohomology operations
25. The kinvariants 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 EilenbergZilber theorem
30. Cup, Pontryagin, and cap products; twisting cochains
31. Brown's theorem
32. The Serre spectral sequence
Bibliographical notes on chapter VI
BIBLIOGRAPHY
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. EILENBERGMACLANE COMPLEXES AND POSTNIKOV SYSTEMS
22. Simplicial Abelian groups
23. EilenbergMacLane complexes
24. K(rr, n)'s and cohomology operations
25. The kinvariants 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 EilenbergZilber 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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