Abstract
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.
Original language | English (US) |
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Pages (from-to) | 2352-2388 |
Number of pages | 37 |
Journal | Journal of Topology |
Volume | 15 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2022 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.