Canonical triangulations of Dehn fillings of the Borromean rings link complement

Abstract

The set of canonical decompositions of a cusped hyperbolic 3-manifold is a complete topological invariant. However, there are only a handful of infinite families for which canonical decompositions are known. In this paper, we find canonical triangulations for Dehn fillings of the Borromean rings link complement and two related manifolds obtained by half-twists. The underlying triangulations were shown to be geometric by Ham and Purcell. To obtain canonical triangulations, we show a local convexity result at every face of the geometric triangulation.