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Author:   Yves Felix ,  Stephen Halperin ,  J.-C. Thomas
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2001 ed.
Volume:   205
Dimensions:   Width: 15.50cm , Height: 3.10cm , Length: 23.50cm
Weight:   2.200kg
ISBN:  

9780387950686

ISBN 10:   0387950680
Pages:   539
Publication Date:   21 December 2000
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

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.- 36Lie algebras of finite depth.- 37 Cell Attachments.- 38 Poincaré Duality.- 39 Seventeen Open Problems.- References.

Reviews

From the reviews: <p>MATHEMATICAL REVIEWS <p> In 535 pages, the authors give a complete and thorough development of rational homotopy theory as well as a review (of virtually) all relevant notions of from basic homotopy theory and homological algebra. This is a truly remarkable achievement, for the subject comes in many guises. <p>Y. Felix, S. Halperin, and J.-C. Thomas <p>Rational Homotopy Theory <p> A complete and thorough development of rational homotopy theory as well as a review of (virtually) all relevant notions from basic homotopy theory and homological algebra. This is truly a magnificent achievement . . . a true appreciation for the goals and techniques of rational homotopy theory, as well as an effective toolkit for explicit computation of examples throughout algebraic topology. <p>a AMERICAN MATHEMATICAL SOCIETY

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