有理同伦论
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作者（法）菲利克斯 著
出版社世界图书出版公司
ISBN9787510058349
出版时间2013-03
装帧平装
开本其他
定价99元
货号23301844
上书时间2024-11-18
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导语摘要
R，ational homotopy theory has the disadvantage of discarding aconsiderable amount of information. For example， the homotopygroups of the sphere S'2 are non-zero in infinitelv many degreeswhereas its rational homotopy groups vanish in all degrees above 3.By contrast， rational homotopy theory has the advantage of beingremarkably computational. For example， there is not even aconjectural de*ion of all the homotopy groups of any simplyconnect.ed finite CW complex， whereas for many of these therational groups can be explicitly determined. And whilerational homotopy theory is indeed simpler than ordinary homotopytheory， it is exactly this simplicity that makes it possible toaddress （if not alway-s to solve） a number of fundamentalquestions.
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
内容摘要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 de*ion 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.
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《有理同伦论(英文)》由世界图书出版公司北京公司出版。
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