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.

中文翻译：

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无限多个虚拟几何三角剖分

我们证明了每个尖点双曲 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，在这个封面中，每一个尖点的长德恩填充都允许无限多的几何理想三角剖分。除了可能具有独立兴趣的新的共轭可分定理之外，该覆盖分几个阶段构建，使用关于外围子群及其双陪集的可分性的结果。几何三角剖分的无限序列在与一个尖点相关的几何子流形中得到支持，并且可以组织成 Pachner 移动的无限三价树。