| 书目名称 | Hyperbolic Manifolds and Discrete Groups | | 编辑 | Michael Kapovich | | 视频video | | | 概述 | Includes beautiful illustrations, a rich set of examples of key concepts, numerous exercises.An extensive bibliography and index are complemented by a glossary of terms.Presents the first complete pro | | 丛书名称 | Modern Birkhäuser Classics | | 图书封面 |  | | 描述 | The main goal of the book is to present a proof of the following. Thurston‘s Hyperbolization Theorem ("The Big Monster"). Suppose that M is a compact atoroidal Haken 3-manifold that has zero Euler characteristic. Then the interior of M admits a complete hyperbolic metric of finite volume. This theorem establishes a strong link between the geometry and topology 3 of 3-manifolds and the algebra of discrete subgroups of Isom(JH[ ). It completely changed the landscape of 3-dimensional topology and theory of Kleinian groups. Further, it allowed one to prove things that were beyond the reach of the standard 3-manifold technique as, for example, Smith‘s conjecture, residual finiteness of the fundamental groups of Haken manifolds, etc. In this book we present a complete proof of the Hyperbolization Theorem in the "generic case." Initially we planned 1 including a detailed proof in the remaining case of manifolds fibered over § as well. However, since Otal‘s book [Ota96] (which treats the fiber bundle case) became available, only a sketch of the proof in the fibered case will be given here. | | 出版日期 | Book 20101st edition | | 关键词 | 3-dimensional topology; Compactification; Group theory; Homeomorphism; Kleinian groups; Otal‘s proof; Rips | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-8176-4913-5 | | isbn_softcover | 978-0-8176-4912-8 | | isbn_ebook | 978-0-8176-4913-5Series ISSN 2197-1803 Series E-ISSN 2197-1811 | | issn_series | 2197-1803 | | copyright | Birkhäuser Boston 2010 |
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发表于 2025-3-21 16:29:58
