Abstract

(Joint with Henry Segerman.) It is a theorem of Moise that every three-manifold admits a triangulation, and this infinitely many. So, it will be difficult to learn anything really interesting about the three-manifold from most of its triangulations. Thurston introduced ``ideal triangulations’’ for studying manifolds with torus boundary; Lackenby introduced ``taut ideal triangulations’’ for studying the Thurston norm ball; Agol introduced ``veering triangulations’’ for studying punctured surface bundles over the circle. Veering triangulations are very rigid; one current conjecture is that a three-manifold admits only finitely many veering triangulations.

After giving an overview of these ideas, we will introduce ``veering Dehn surgery’’. We use this to give the first infinite families of veering triangulations with various interesting properties.