Abstract:

Every half-translation surface induces a singular flat metric. A saddle connection on an half-translation surface is an open geodesic segment which connects singular points and which contains no singular points in the interior. The saddle connection graph is a graph whose vertices are saddle connections and edges are pairs of disjoint saddle connections. In this talk, we will discuss the geometry of saddle connection graphs. We will show that on the one hand saddle connection grpahs are isometrically rigid, namely two saddle connection graphs are isometric if and only if the underlying half-translation surfaces are affine equivalent. While on the other hand all saddle connections graphs are uniformly quasi-isometric to the regular countably infinite-valent tree. This talk is partially based on a joint work with Valentina Disarlo, Anja Rendecker and Robert Tang. 

ID：653 2910 3639

Code：175707