Combinatorics of Triangulations and Volume Optimisation
by Stephan Tillmann
Abstract: In previous work, Luo defined a volume function on the space of circle-valued angle structures on a triangulated 3-manifold. He showed that smooth critical points of the volume function yield solutions of a generalised version of Thurston's hyperbolic gluing equations. In this talk, I will report on joint work with Luo in which we show that non-smooth critical points have strong consequences on the topology of the 3-manifold. The proof is mainly combinatorial and involves a new class of triangulations that combines a weak version of 0-efficiency with a weak version of minimality.