The mapping class group of the plane minus a Cantor set arises naturally in the study of group actions on the plane by homeomorphisms. The ray graph is a Gromov-hyperbolic graph on which this group acts by isometries (it is an equivalent of the curve graph for this surface of infinite type). Therefore, studying the properties of the ray graph could give tools to study subgroups of the considered mapping class group and prevent some specific group actions on the plane.

In a recent joint work with Alden Walker, we give a description of the Gromov boundary of the ray graph in terms of "cliques of long geodesic rays" on the plane minus a Cantor set. As a consequence, we prove that the Gromov boundary of the ray graph is homeomorphic to a quotient of a subset of the circle. In this talk, I will introduce the ray graph and present (with many pictures!) our description of its Gromov boundary. Speaker(s): Juliette Bavard (University of Chicago)