Infinitely many virtual geometric triangulations

Dave Futer (Temple)

Abstract: Every cusped hyperbolic 3-manifold should admit a decomposition into a union of positively oriented ideal tetrahedra. Somewhat shockingly, the question of whether such a geometric triangulation exists is still open. Luo, Schleimer, and Tillmann proved that geometric ideal triangulations of this sort exist in some cover of every cusped 3-manifold. We extend their result by showing that every cusped hyperbolic 3-manifold has a single cover admitting infinitely many geometric ideal triangulations. The proof involves double coset separability of peripheral subgroups. This is joint work with Neil Hoffman.