Title: Spinning, Straightening and the Recognition of Closed Hyperbolic 3-Manifolds
Speaker: Stephan Tillmann (UQ)
Abstract: I'll talk about joint work with Feng Luo (Rutgers) and Tian Yang (Rutgers) on using Thurston's hyperbolic gluing equations in the context of triangulations of closed 3-manifolds: We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are Thurston's spinning construction and a volume rigidity result attributed by Dunfield to Thurston, Gromov and Goldman. As an application, together with work of Francaviglia, this greatly simplifies the rigorous algorithmic detection and description of hyperbolic structures on closed 3-manifolds due to Casson and Manning.