Rational Homotopy Theory

Rational Homotopy Theory by Yves Felix, Stephen Halperin, J.-C. Thomas.

as well as by the list of open problems in the final section of this monograph. The computational power of rational homotopy theory is due to the discovery by Quillen [135] and by Sullivan [144] of an explicit algebraic formulation. In each case the rational homotopy type of a topological space is t...

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Bibliographic Details
Main Authors: Felix, Yves (Author), Halperin, Stephen (Author), Thomas, J.-C (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2001.
Edition:1st ed. 2001.
Series:Graduate Texts in Mathematics, 205
Springer eBook Collection.
Subjects:
Algebraic topology.
Electronic resources (E-books)
Online Access:Click to view e-book
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Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I Homotopy Theory, Resolutions for Fibrations, and P- local Spaces
  • 0 Topological spaces
  • 1 CW complexes, homotopy groups and cofibrations
  • 2 Fibrations and topological monoids
  • 3 Graded (differential) algebra
  • 4 Singular chains, homology and Eilenberg-MacLane spaces
  • 5 The cochain algebra C*(X;$$ Bbbk $$
  • 6 (R, d)— modules and semifree resolutions
  • 7 Semifree cochain models of a fibration
  • 8 Semifree chain models of a G—fibration
  • 9 P local and rational spaces
  • II Sullivan Models
  • 10 Commutative cochain algebras for spaces and simplicial sets
  • 11 Smooth Differential Forms
  • 12 Sullivan models
  • 13 Adjunction spaces, homotopy groups and Whitehead products
  • 14 Relative Sullivan algebras
  • 15 Fibrations, homotopy groups and Lie group actions
  • 16 The loop space homology algebra
  • 17 Spatial realization
  • III Graded Differential Algebra (continued)
  • 18 Spectral sequences
  • 19 The bar and cobar constructions
  • 20 Projective resolutions of graded modules
  • IV Lie Models
  • 21 Graded (differential) Lie algebras and Hopf algebras
  • 22 The Quillen functors C* and C
  • 23 The commutative cochain algebra, C*(L,dL)
  • 24 Lie models for topological spaces and CW complexes
  • 25 Chain Lie algebras and topological groups
  • 26 The dg Hopf algebra C*(?X
  • V Rational Lusternik Schnirelmann Category
  • 27 Lusternik-Schnirelmann category
  • 28 Rational LS category and rational cone-length
  • 29 LS category of Sullivan algebras
  • 30 Rational LS category of products and flbrations
  • 31 The homotopy Lie algebra and the holonomy representation
  • VI The Rational Dichotomy: Elliptic and Hyperbolic Spaces and Other Applications
  • 32 Elliptic spaces
  • 33 Growth of Rational Homotopy Groups
  • 34 The Hochschild-Serre spectral sequence
  • 35 Grade and depth for fibres and loop spaces
  • 36 Lie algebras of finite depth
  • 37 Cell Attachments
  • 38 Poincaré Duality
  • 39 Seventeen Open Problems
  • References.

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