Rational Homotopy Theory - Felix, Yves

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Résumé :
Rational homotopy theory is a subfield of algebraic topology. It has been an active area for more than 30 years, and no attempt has been made at writing a textbook in more than 15 years. Both notation and techniques of rational homotopy theory have been considerably simplified over the past 15 years, so that the older books in are already out of date. All three authors are considered to be among the leading experts in rational homotopy theory....

Sommaire:
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; dollars dollars\Bbbk dollars dollars.- 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.- 36Lie algebras of finite depth.- 37 Cell Attachments.- 38 Poincar? Duality.- 39 Seventeen Open Problems.- References.