无限多个虚拟几何三角形

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2022-11-01 DOI:10.1112/topo.12271

David Futer, Emily Hamilton, Neil R. Hoffman

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引用次数: 2

摘要

证明了每一个凸双曲3流形都有一个有限覆盖，允许无限多个几何理想三角剖分。此外，该盖上每一个尖点的长Dehn填充都允许无限多个几何理想三角剖分。利用关于外围子群及其重伴集的可分性的结果，以及可能引起独立兴趣的一个新的共轭可分性定理，分几个阶段构造了这个盖。几何三角形的无限序列被支持在与一个顶点相关的几何子流形中，并且可以组织成一个无限的Pachner移动三价树。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Infinitely many virtual geometric triangulations

We prove that every cusped hyperbolic 3-manifold has a finite cover admitting infinitely many geometric ideal triangulations. Furthermore, every long Dehn filling of one cusp in this cover admits infinitely many geometric ideal triangulations. This cover is constructed in several stages, using results about separability of peripheral subgroups and their double cosets, in addition to a new conjugacy separability theorem that may be of independent interest. The infinite sequence of geometric triangulations is supported in a geometric submanifold associated to one cusp, and can be organized into an infinite trivalent tree of Pachner moves.

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.