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J. P. May

Simplicial Objects in Algebraic Topology

170 pages,  5-12 x 8-12  © 1967
Series: Chicago Lectures in Mathematics

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
Subjects



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