Stephan Tillmann | Canonical cell decompositions for punctured real projective surfaces

5/7/2021 FRG Workshop on Geometric Methods for Analyzing Discrete Shapes

Speaker: Stephan Tillmann

Title: Canonical cell decompositions for punctured real projective surfaces

Abstract: Cooper and Long generalised the canonical cell decoposition of decorated cusped hyperbolic manifolds of finite volume to the setting of real projective geometry. In this talk, I will describe an edge-flipping calgorithm that computes these decompositions for punctured surfaces using Fock and Goncharov's A-coordinates.
If time permits, I will also outline how this setting allows us to show that the moduli space of doubly-decorated convex projective structures of finite volume on punctured surfaces has a natural cell decomposition of this space that is invariant under the action of the mapping class group. This generalises a result of Penner concerning decorated Teichmüller space. All of this is join work with Robert Haraway, Robert Löwe and Dominic Tate.