Graphs of curves and arcs quasi-isometric to big mapping class groups

This is the second of two talks recorded for 2021's Nearly Carbon Neutral Geometry Topology Conference.

Abstract: Building on the work of Mann and Rafi, this video gives examples of big mapping class groups that are quasi-isometric to graphs of curves and arcs. In particular, the mapping class group of the punctured Cantor tree is shown to be quasi-isometric to that surface's loop graph, and the mapping class groups of "translatable surfaces" are shown to be quasi-isometric to the "translatable curve graph". This latter result is a classification, in the sense that only translatable surfaces are quasi-isometric to a curve graph of any kind.

References: