Rational Homotopy Theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2001
|
| Series: | Graduate Texts in Mathematics
205 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (XXXIII, 539 p) |
| ISBN: | 9781461301059 9781461265160 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4613-0105-9 |
Staff View
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| 500 | |a 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 | ||
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Record in the Search Index
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461301059 9781461265160 |
| issn | 0072-5285 |
| language | English |
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| spelling | Félix, Yves 1951- Verfasser (DE-588)111765560 aut Rational Homotopy Theory by Yves Félix, Stephen Halperin, Jean-Claude Thomas New York, NY Springer New York 2001 1 Online-Ressource (XXXIII, 539 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 205 0072-5285 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 Mathematics Algebraic topology Algebraic Topology Mathematik Rationale Homotopietheorie (DE-588)4177003-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s 1\p DE-604 Rationale Homotopietheorie (DE-588)4177003-1 s 2\p DE-604 Halperin, Stephen 1942- Sonstige (DE-588)119201852 oth Thomas, Jean-Claude Sonstige (DE-588)173448909 oth https://doi.org/10.1007/978-1-4613-0105-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Félix, Yves 1951- Rational Homotopy Theory Mathematics Algebraic topology Algebraic Topology Mathematik Rationale Homotopietheorie (DE-588)4177003-1 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4177003-1 (DE-588)4128142-1 |
| title | Rational Homotopy Theory |
| title_auth | Rational Homotopy Theory |
| title_exact_search | Rational Homotopy Theory |
| title_full | Rational Homotopy Theory by Yves Félix, Stephen Halperin, Jean-Claude Thomas |
| title_fullStr | Rational Homotopy Theory by Yves Félix, Stephen Halperin, Jean-Claude Thomas |
| title_full_unstemmed | Rational Homotopy Theory by Yves Félix, Stephen Halperin, Jean-Claude Thomas |
| title_short | Rational Homotopy Theory |
| title_sort | rational homotopy theory |
| topic | Mathematics Algebraic topology Algebraic Topology Mathematik Rationale Homotopietheorie (DE-588)4177003-1 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Mathematics Algebraic topology Algebraic Topology Mathematik Rationale Homotopietheorie Homotopietheorie |
| url | https://doi.org/10.1007/978-1-4613-0105-9 |
| work_keys_str_mv | AT felixyves rationalhomotopytheory AT halperinstephen rationalhomotopytheory AT thomasjeanclaude rationalhomotopytheory |