The structure of groups with a quasiconvex hierarchy:
This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory generalizing ideas from t...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton ; Oxford
Princeton University Press
[2021]
|
| Schriftenreihe: | Annals of mathematics studies
Number 209 |
| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FHR01 FKE01 FLA01 TUM01 UBW01 UBY01 UPA01 Volltext |
| Zusammenfassung: | This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory generalizing ideas from the 1960s, a version of Dehn Filling that functions in the category of special cube complexes, and a variety of results about right-angled Artin groups. The book culminates by establishing a remarkable theorem about the nature of hyperbolic groups that are constructible as amalgams.The applications described here include the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly, this work establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds, and validates this program in significant cases. Illustrated with more than 150 color figures, this book will interest graduate students and researchers working in geometry, algebra, and topology |
| Beschreibung: | Bandzählung laut die Webseite : 366 |
| Beschreibung: | 1 Online-Ressource (x, 357 Seiten) Illustrationen, Diagramme |
| ISBN: | 9780691213507 |
| DOI: | 10.1515/9780691213507 |
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| index_date | 2024-07-03T17:25:43Z |
| indexdate | 2024-07-10T09:08:29Z |
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| isbn | 9780691213507 |
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| spelling | Wise, Daniel T. 1971- (DE-588)1030054231 aut The structure of groups with a quasiconvex hierarchy Daniel T. Wise Princeton ; Oxford Princeton University Press [2021] © 2021 1 Online-Ressource (x, 357 Seiten) Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier Annals of mathematics studies Number 209 Bandzählung laut die Webseite : 366 This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory generalizing ideas from the 1960s, a version of Dehn Filling that functions in the category of special cube complexes, and a variety of results about right-angled Artin groups. The book culminates by establishing a remarkable theorem about the nature of hyperbolic groups that are constructible as amalgams.The applications described here include the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly, this work establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds, and validates this program in significant cases. Illustrated with more than 150 color figures, this book will interest graduate students and researchers working in geometry, algebra, and topology MATHEMATICS / Group Theory bisacsh Group theory Hyperbolic groups Erscheint auch als Druck-Ausgabe 978-0-691-17044-2 Annals of mathematics studies Number 209 (DE-604)BV040389493 209 https://doi.org/10.1515/9780691213507 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Wise, Daniel T. 1971- The structure of groups with a quasiconvex hierarchy Annals of mathematics studies MATHEMATICS / Group Theory bisacsh Group theory Hyperbolic groups |
| title | The structure of groups with a quasiconvex hierarchy |
| title_auth | The structure of groups with a quasiconvex hierarchy |
| title_exact_search | The structure of groups with a quasiconvex hierarchy |
| title_exact_search_txtP | The structure of groups with a quasiconvex hierarchy |
| title_full | The structure of groups with a quasiconvex hierarchy Daniel T. Wise |
| title_fullStr | The structure of groups with a quasiconvex hierarchy Daniel T. Wise |
| title_full_unstemmed | The structure of groups with a quasiconvex hierarchy Daniel T. Wise |
| title_short | The structure of groups with a quasiconvex hierarchy |
| title_sort | the structure of groups with a quasiconvex hierarchy |
| topic | MATHEMATICS / Group Theory bisacsh Group theory Hyperbolic groups |
| topic_facet | MATHEMATICS / Group Theory Group theory Hyperbolic groups |
| url | https://doi.org/10.1515/9780691213507 |
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