Coarse vs fine geometry of the saddle connection graph

Abstract: The saddle connection graph encodes intersection information regarding saddle connections on a translation surface. This can be viewed as an induced subgraph of the arc graph of the surface. A natural question to ask is what we can deduce from either the isomorphism type or the quasi-isometry type of the saddle connection graph. It turns out that there is a quite a difference between the fine and coarse geometry. Both parts are based on joint work with Valentina Disarlo, Huiping Pan, and Anja Randecker.

group theory

Audience: researchers in the topic

World of GroupCraft