Georgia Institute of Technology College of Sciences

The mapping class group of the plane minus a Cantor set naturally appears in many dynamical contexts, including group actions on surfaces, the study of groups of homeomorphisms on a Cantor set, and complex dynamics. In this talk, I will present the 'ray graph', which is a Gromov-hyperbolic graph on which this big mapping class group acts by isometries (it is an equivalent of the curve graph for this surface of infinite topological type). If time allows, I will give a description of the Gromov-boundary of the ray graph in terms of long rays in the plane minus a Cantor set. This involves joint work with Alden Walker.