The Geometry and Topology of Coxeter Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
2007
|
| Schriftenreihe: | London Mathematical Society Monographs
32 |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Beschreibung: | Biographical note: DavisMichael W.: Michael W. Davis is professor of mathematics at Ohio State University Main description: The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures |
| Beschreibung: | 1 Online-Ressource (600 S.) |
| ISBN: | 9781400845941 |
| DOI: | 10.1515/9781400845941 |
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| isbn | 9781400845941 |
| language | English |
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| spelling | Davis, Michael W. Verfasser aut The Geometry and Topology of Coxeter Groups Princeton, N.J. Princeton University Press 2007 1 Online-Ressource (600 S.) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society Monographs 32 Biographical note: DavisMichael W.: Michael W. Davis is professor of mathematics at Ohio State University Main description: The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures Geometrie (DE-588)4020236-7 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Coxeter-Gruppe (DE-588)4261522-7 gnd rswk-swf Coxeter-Gruppe (DE-588)4261522-7 s Algebraische Topologie (DE-588)4120861-4 s 1\p DE-604 Geometrie (DE-588)4020236-7 s 2\p DE-604 https://doi.org/10.1515/9781400845941 Verlag Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400845941&searchTitles=true 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 | Davis, Michael W. The Geometry and Topology of Coxeter Groups Geometrie (DE-588)4020236-7 gnd Algebraische Topologie (DE-588)4120861-4 gnd Coxeter-Gruppe (DE-588)4261522-7 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4120861-4 (DE-588)4261522-7 |
| title | The Geometry and Topology of Coxeter Groups |
| title_auth | The Geometry and Topology of Coxeter Groups |
| title_exact_search | The Geometry and Topology of Coxeter Groups |
| title_full | The Geometry and Topology of Coxeter Groups |
| title_fullStr | The Geometry and Topology of Coxeter Groups |
| title_full_unstemmed | The Geometry and Topology of Coxeter Groups |
| title_short | The Geometry and Topology of Coxeter Groups |
| title_sort | the geometry and topology of coxeter groups |
| topic | Geometrie (DE-588)4020236-7 gnd Algebraische Topologie (DE-588)4120861-4 gnd Coxeter-Gruppe (DE-588)4261522-7 gnd |
| topic_facet | Geometrie Algebraische Topologie Coxeter-Gruppe |
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