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

Abstract

We describe sucient conditions which guarantee that a nite 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 Teichmuller space is a quasi- isometric embedding for both of the standard metrics. As a consequence, we produce innitely 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 Teichmuller space.