## Verified canonical triangulations of hyperbolic 3-manifolds

Neil Hoffman (Melbourne)

Abstract

A 3-manifold can be decomposed into a set of n tetrahedra whose faces are identified in pairs. In this case, we say the set of tetrahedra and the face pairs are a triangulation for the 3-manifold. In the case that the 3-manifold M admits a hyperbolic structure, one can often find a canonical triangulation for M. This talk will describe a specific implementation of Epstein and Penner's algorithm that can rigorously compute a canonical triangulation of a hyperbolic 3-manifold under some mild constraints. This will be followed by some interesting consequences of the successful computations and a discussion of how possible ways to relax the constraints currently required by the algorithm. This is joint work with Nathan Dunfield and Joan Licata (see arXiv:1407.7827).