The geometry of right-angled Artin subgroups of mapping class groups

Abstract

We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. Moreover, under these conditions, the orbit map to Teichmüller space is a quasi-isometric embedding for both of the standard metrics. As a consequence, we produce infinitely many genus $h$ surfaces (for any $h$ at least 2) in the moduli space of genus $g$ surfaces (for any $g$ at least 3) for which the universal covers are quasi-isometrically embedded in the Teichmüller space.