Large-scale geometry of the saddle connection graph

Anja Randecker
Heidelberg University
https://www.mathi.uni-heidelberg.de/~arandecker/

Date(s) : 18/12/2020 iCal
11h00 - 12h00

For a half-translation surface, the saddle connection graph is the induced subgraph of the arc graph where vertices are saddle connections.
On the one hand, saddle connection graphs are rigid in the sense that every isometry is induced by an affine diffeomorphism of the underlying half-translation surface.
On the other hand, all saddle connection graphs are uniformly quasi-isometric to the infinite valence tree, so they are not distinguishable from the coarse geometry point of view.

In this talk, I will focus on the coarse geometry: I will explain the arguments for the uniform quasi-isometry and will hint at how the (coarse concept) Gromov boundary can still hold valuable insight.
The results can be found in arXiv:2011.12975 which is joint work with Valentina Disarlo, Huiping Pan, and Robert Tang.