Work

Infinitely many virtual geometric triangulations

Year: 2022

Type: article

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.

Source: Journal of Topology

DOI: 10.1112/topo.12271

Authors: David Futer, Emily Hamilton, Neil R. Hoffman

Institutions: Temple University, California Polytechnic State University, Oklahoma State University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Foundation

Awards: Hyperbolic Manifolds and Their Groups, G789609860