Geometric models for infinite-type surface mapping class groups

Michael Kopreski (Bilbao)

Abstract: Let S be an infinite-type surface and let G < Map(S) be a locally bounded Polish subgroup. We construct a metric graph M of simple arcs and curves on S preserved by the action of G and for which the vertex orbit map is a coarse equivalence; moreover, if G is boundedly generated, then the orbit map is a quasi-isometry. We show that if S contains a non-displaceable subsurface and G > PMap_c(S) is boundedly generated or G = Map(S) and is locally bounded, then asdim M = asdim G is infinite.