Title:
Mapping class groups of infinite-type surfaces and their actions on hyperbolic graphs
Abstract:
Given a finite-type surface, there are two important objects naturally associated to it. The first is the mapping class group and the second is the curve graph, which the mapping class group acts on via isometries. This action is well understood and has been extremely useful in understanding the algebraic and geometric properties of mapping class groups. There has been a recent surge in studying surfaces of infinite type and in this talk we shift our focus to their mapping class groups. I’ll discuss recent joint work with Carolyn Abbott and Nicholas Miller explicitly constructing “intrinsically infinite-type” mapping classes that act as loxodromic isometries on the relative arc graph (the appropriate graph in this setting).