Bounded combinatorics and uniform models for hyperbolic 3‐manifolds
Bounded combinatorics and uniform models for hyperbolic 3‐manifolds
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双曲 3 流形的有界组合和统一模型
DOI：
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发表时间：
2013
期刊：
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通讯作者：
J. Souto
中科院分区：
文献类型：
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作者：
Jeffrey F. Brock;Y. Minsky;Hossein Namazi;J. Souto
有界型 3 流形作为从有限列表中选择的不可约 3 流形的组合有界粘合而出现。我们证明了对于一大类有界类型和大粘合高度的 3 流形来说，有效的双曲线化和有效的刚性。具体来说，我们展示了有界类型和大高度的3-流形上双曲度量的存在性和唯一性，并证明了根据不可约流形列表、识别拓扑和粘合映射的组合明确描述的组合模型的bilipschitz微分同胚的存在性。
Bounded‐type 3‐manifolds arise as combinatorially bounded gluings of irreducible 3‐manifolds chosen from a finite list. We prove effective hyperbolization and effective rigidity for a broad class of 3‐manifolds of bounded type and large gluing heights. Specifically, we show the existence and uniqueness of hyperbolic metrics on 3‐manifolds of bounded type and large heights, and prove existence of a bilipschitz diffeomorphism to a combinatorial model described explicitly in terms of the list of irreducible manifolds, the topology of the identification, and the combinatorics of the gluing maps.