Triangulated cores of punctured-torus groups

Abstract

We show that the interior of the convex core of a quasifuchsian punctured-torus group admits an ideal decomposition (usually an infinite triangulation) which is canonical in two very different senses: in a combinatorial sense via the pleating invariants, and in a geometric sense via an Epstein-Penner convex hull construction in Minkowski space. This result re-proves the Pleating Lamination Theorem for quasifuchsian punctured-torus groups, and extends to all punctured-torus groups if a strong version of the Pleating Lamination Conjecture is true.