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Synopsis
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homotopy theory have been considerably simplified over the past 15 years, so that the older books in are already out of date.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.
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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
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Rational Homotopy Theory (eng)
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Rational Homotopy Theory: 205 (Graduate Texts in Mathematics)
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Rational Homotopy Theory
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Rational Homotopy Theory
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Springer New York Okt 2012, 2012
ISBN 10: 1461265169
ISBN 13: 9781461265160
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Rational homotopy theory is a subfield of algebraic topology. Written by three authorities in the field, this book contains all the main theorems of the field with complete proofs. As both notation and techniques of rational homotopy theory have been considerably simplified, the book presents modern elementary proofs for many results that were proven ten or fifteen years ago. 588 pp. Englisch. Seller Inventory # 9781461265160
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Rational Homotopy Theory (Graduate Texts in Mathematics, 205)
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Rational Homotopy Theory
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Rational homotopy theory is a subfield of algebraic topology. Written by three authorities in the field, this book contains all the main theorems of the field with complete proofs. As both notation and techniques of rational homotopy theory have been con. Seller Inventory # 4189165
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Rational Homotopy Theory
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Rational Homotopy Theory
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Rational Homotopy Theory
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9781461265160