Overview
- Authors:
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Yves Félix
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Institut Mathematiques, Universite de Louvain La Neuve, Louvain-la-Neuve, Belgium
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Stephen Halperin
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College of Computer, Mathematical, and Physical Science, University of Maryland, College Park, USA
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Jean-Claude Thomas
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Faculte des Sciences, Universite d’Angers, Angers, France
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Table of contents (40 chapters)
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Front Matter
Pages i-xxxii
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Homotopy Theory, Resolutions for Fibrations, and P-local Spaces
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Front Matter
Pages xxxiii-xxxiii
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 1-3
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 4-22
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 23-39
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 40-50
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 51-64
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 65-67
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 68-76
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 77-87
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 88-101
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 102-114
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Sullivan Models
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 115-130
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 131-137
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 138-164
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 165-180
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 181-194
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 195-222
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- Yves Félix, Stephen Halperin, Jean-Claude Thomas
Pages 223-236
About this book
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 the same as the isomorphism class of its algebraic model and the rational homotopy type of a continuous map is the same as the algebraic homotopy class of the correspond ing morphism between models. These models make the rational homology and homotopy of a space transparent. They also (in principle, always, and in prac tice, sometimes) enable the calculation of other homotopy invariants such as the cup product in cohomology, the Whitehead product in homotopy and rational Lusternik-Schnirelmann category. In its initial phase research in rational homotopy theory focused on the identi of these models. These included fication of rational homotopy invariants in terms the homotopy Lie algebra (the translation of the Whitehead product to the homo topy groups of the loop space OX under the isomorphism 11'+1 (X) ~ 1I.(OX», LS category and cone length. Since then, however, work has concentrated on the properties of these in variants, and has uncovered some truly remarkable, and previously unsuspected phenomena. For example • If X is an n-dimensional simply connected finite CW complex, then either its rational homotopy groups vanish in degrees 2': 2n, or else they grow exponentially.
Reviews
From the reviews:
MATHEMATICAL REVIEWS
"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."
Y. Felix, S. Halperin, and J.-C. Thomas
Rational Homotopy Theory
"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."
—AMERICAN MATHEMATICAL SOCIETY
Authors and Affiliations
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Institut Mathematiques, Universite de Louvain La Neuve, Louvain-la-Neuve, Belgium
Yves Félix
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College of Computer, Mathematical, and Physical Science, University of Maryland, College Park, USA
Stephen Halperin
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Faculte des Sciences, Universite d’Angers, Angers, France
Jean-Claude Thomas