Title: Angle structures for veering triangulations
Abstract: Casson and Rivin have proposed a program to explicitly construct the finite-volume hyperbolic metric on a 3-manifold given as a combinatorial triangulation: namely, find dihedral angles for the tetrahedra, subject to certain gluing conditions. These angles are hard to find in general, and solving a linearized version of the problem (finding an “angle structure”) already has strong topological implications. Agol recently introduced a class of “veering” triangulations with pleasant existence and uniqueness properties. We will prove these triangulations admit angle structures, and explain some context and refinements. Joint work with Francois Gueritaud.