目錄
Introduction
Table of Examples
Ⅰ Homotopy Theory, Resolutions for Fibrations, and Plocal Spaces
0 Topological spaces
1 CW complexes, homotopy groups and coflbrations
(a) CW complexes
(b) Homotopy groups
(c) Weak homotopy type
(d) Cofibrations and NDR pairs
(e) Adjunction spaces
(f) Cones, suspensions, joins and smashes
2 Fibrations and topological monoids
(a) Fibrations
(b) Topological monoids and G-fibrations
(c) The homotopy fibre and the holonomy action
(d) Fibre bundles and principal bundles
(e) Associated bundles, classifying spaces, the Borel construction and the holonomy fibration
3 Graded (differential) algebra
(a) Graded modules and complexes
(b) Graded algebras
(c) Differential graded algebras
(d) Graded coalgebras
(e) When k is a field
4 Singular chains, homology and Eilenberg-MacLane spaces
(a) Basic definitions, (normalized) singular chains
(b) Topological products, tensor products and the dgc, C*(X;k)
(c) Pairs, excision, homotopy and the Hurewicz homomorphism
(d) Weak homotopy equivalences
(e) Cellular homology and the Hurewicz theorem
(f) Eilenberg-MacLane spaces
5 The cochain algebra C*(X;k)
6 (R,d)-modules and semifree resolutions
(a) Semifree models
(b) Quasi-isomorphism theorems
7 Semifree cochain models of a flbration
8 Semifree chain models of a G-flbration
(a) The chain algebra of a topological monoid
(b) Semifree chain models
(c) The quasi-isomorphism theorem
(d) The Whitehead-Serre theorem
9 p-local and rational spaces
(a) p-local spaces
(b) Localization
(e) Rational homotopy type
Ⅱ Sullivan Models
Ⅲ Graded Differential Algebra (continued)
Ⅳ Lie Models
Ⅴ Rational Lusternik Schnirelmann Category
Ⅵ The Rational Dichotomy
References
Index
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