作者：菲利克斯
页数：535
出版社：世界图书出版公司
出版日期：2013
ISBN：9787510058349
电子书格式：pdf/epub/txt
内容简介
本书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。目次：（一）同伦理论、纤维化结果和P局部空间：拓扑空间；CW复数，同伦群和上纤维化；纤维化和拓扑独异点；阶化代数；奇异链、同调和Eilenberg-Maclane空间；上链代数C最(X;k)；（R，d）模和半自由解；纤维化的半自由上链模；G-纤维化的半自由链模；P-局部和有理空间；（二）Sullivan模：空间的交换上链代数和简化集；光滑微分形式；Sullivan模；黏着空间、同伦群和Whitehead乘积；相对Sullivan代数；纤维化、同伦群和李群行为；环空间同伦代数；空间现实；（三）阶化微分代数：谱序列；阶化模的映射解；（四）李模：阶化李代数和Hopf代数；Quillen因子的C最和￡；交换上链代数；拓扑空间和CW复形；链李代数和拓扑群；dg Hopf代数；（五）有理Lusternik Schnirelmann范畴；有理LS范畴和有理锥长度；Sullivan代数的LS范畴；乘积的有理LS范畴和纤维丛；同伦里代数和完整表示；（六）有理二分：椭圆和双曲空间和其他应用：椭圆空间；有理同伦群增长；Hochachild-Serre谱序列；纤维和环空间的分级和深； 有限深李代数；细胞粘附；Poincare对偶；十七开放问题。
作者简介
Yves Félix, Stephen Halperin, Jean-Claude Thomas是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
本书特色
r，ational homotopy theory has the disadvantage of discarding a
considerable amount of information. for example， the homotopy
groups of the sphere s’2 are non-zero in infinitelv many degrees
whereas its rational homotopy groups vanish in all degrees above 3.
by contrast， rational homotopy theory has the advantage of being
remarkably computational. for example， there is not even a
conjectural description of all the homotopy groups of any simply
connect.ed finite cw complex， whereas for many of these the
rational groups can be explicitly determined. and while
rational homotopy theory is indeed simpler than ordinary homotopy
theory， it is exactly this simplicity that makes it possible to
address （if not alway-s to solve） a number of fundamental
questions.
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最(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最(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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Article Title:《有理同伦论-(影印版)》
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