菲利克斯所著的《有理同伦论》是讲述有理同伦的教材，有该领域的三位知名作者合著而成。同伦理论是代数拓扑的一个分支，书中讲述了该领域的主要定理和完整证明，并将有理同伦理论的表示和技巧做了大量的简化，书中呈现了许多重要结果的现代证明，这些结果都是十来年的主要贡献。

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