Speaker: Francois Gueritaud, University of Southern California
Title of talk: Triangulating the convex core ofquasifuchsian once-punctured torus groups
Abstract: Let $\Gamma \subset \text{Isom}^+(\mathbb{H}^3)$ be a discrete free subgroup generated by two elementswith parabolic commutator. Generically, the manifold$\mathbb{H}^3/\Gamma$ has a convex core $C$ whose boundary comes withtwo pleating laminations. These laminations define an infinite(topological) ideal triangulation $T$ of the interior of $C$, which iscanonical in a combinatorial sense. We turn $T$ into a ``true''geometric triangulation via Rivin's maximum volume principle, and showthat $T$ is also canonical in a different, purely geometric sense, aresult first conjectured by Akiyoshi, Sakuma, Wada and Yamashita.