Author | Fรฉlix, Yves. author |
---|---|
Title | Rational Homotopy Theory [electronic resource] / by Yves Fรฉlix, Stephen Halperin, Jean-Claude Thomas |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-0105-9 |
Descript | XXXIII, 539 p. online resource |
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)โ modules and semifree resolutions -- 7 Semifree cochain models of a fibration -- 8 Semifree chain models of a Gโfibration -- 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 Poincarรฉ Duality -- 39 Seventeen Open Problems -- References