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。
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书名 | 有理同伦论 |
分类 | 科学技术-自然科学-数学 |
作者 | (法)菲利克斯 |
出版社 | 世界图书出版公司 |
下载 | ![]() |
简介 | 编辑推荐 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。 目录 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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