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The Structure of Groups with a Quasiconvex Hierarchy : (AMS-209) /
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...
| Autor principal: | |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, NJ :
Princeton University Press,
[2021]
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| Colección: | Annals of Mathematics Studies ;
366 |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo |
| Sumario: | 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. |
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| Descripción Física: | 1 online resource (376 p.) : 166 color illus. |
| ISBN: | 9780691213507 9783110754001 9783110753776 9783110754131 9783110753905 9783110494914 9783110739121 |
| Acceso: | restricted access |