Please join us for the next installment of the Geometry and Topology Seminar for 2025!
SMRI Seminar Room (A12 Room 301)
We give another proof of the following result: the Epstein-Penner ideal cell decomposition of a decorated hyperbolic surface with punctures matches the Bowditch-Epstein ideal cell decomposition. Further, we introduce a generalized notion of the cut locus (also known as spine or collision locus) for decorated crowned hyperbolic surfaces, and show that we naturally get two distinct decompositions of decorated Teichmüller space of surfaces with crowns. Both of them are ideal cell decompositions (this recovers some results of Penner). Finally, we discuss a third decomposition in the setting of decorated ideal hyperbolic polygons.