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Inhaltsangabe
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.
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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
Reseña del editor
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.
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- VerlagSpringer
- Erscheinungsdatum2001
- ISBN 10 0387950680
- ISBN 13 9780387950686
- EinbandTapa dura
- SpracheEnglisch
- Anzahl der Seiten588
- Kontakt zum HerstellerNicht verfügbar
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Rational Homotopy Theory
Verlag:
Springer New York, Springer US Dez 2000, 2000
ISBN 10: 0387950680
ISBN 13: 9780387950686
Neu
Hardcover
Anbieter: buchversandmimpf2000, Emtmannsberg, BAYE, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Buch. Zustand: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 588 pp. Englisch. Artikel-Nr. 9780387950686
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Rational Homotopy Theory (Graduate Texts in Mathematics, 205)
Verlag:
Springer (edition 2001), 2000
ISBN 10: 0387950680
ISBN 13: 9780387950686
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Hardcover. Zustand: Good. 2001. Ship within 24hrs. Satisfaction 100% guaranteed. APO/FPO addresses supported. Artikel-Nr. 0387950680-11-1
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Rational Homotopy Theory
Verlag:
Springer New York, Springer US, 2000
ISBN 10: 0387950680
ISBN 13: 9780387950686
Neu
Hardcover
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Buch. Zustand: 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. Artikel-Nr. 9780387950686
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Rational Homotopy Theory (Graduate Texts in Mathematics, 205)
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Rational Homotopy Theory
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