Infinitely many virtual geometric triangulations. Issue 4 (1st November 2022)

• Record Type: Journal Article
• Authors: Futer, David; Hamilton, Emily; Hoffman, Neil R.
• Is Part Of: Journal of topology. Volume 15:Issue 4(2022)
• Page Start: 2352
• Page End: 2388
• Publication Date: 2022-11-01
• Subjects: Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12271
• Languages: English
• ISSNs: 1753-8416

Abstract

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.