Flipping triangles on surfaces

Hugo Parlier (University of Fribourg)

Abstract: A topological surface with a prescribed set of vertices admits different triangulations with the vertices as the vertices of the triangulation. From a given triangulation, you can get a new one by “flipping” two adjacent triangles. This gives rise to flip graphs: a graph where triangulations are the vertices and flips correspond to edges. These graphs have interesting geometries. When the surface is a polygon, these graphs are finite and their diameters were studied by Sleator-Tarjan-Thurston and more recently by Pournin. In general, flip graphs are quasi-isometric to the underlying mapping class group. The talk will be about different aspects of their geometry including the diameter of the quotient by their autormorphism group. It will be based on joint work with Disarlo and with Pournin.