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The Structure of Groups with a Quasiconvex Hierarchy : (AMS-209).
・ISBN 978-0-691-17045-9 paper US$ 92.00
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| 著者・編者 | Wise, Daniel T., |
|---|---|
| シリーズ | Annals of Mathematics Studies |
| 出版社 | (Princeton University Press, US) |
| 出版年月 | 2021 |
| ページ数 | 376 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-101＞ |
解説
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 that generalizes 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.