Convex cocompactness in mapping class groups via quasiconvexity in right-angled Artin groups

Abstract

© 2016 London Mathematical Society. We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. That is, if the right-angled Artin group G < Mod(S) satisfies certain conditions that imply that G is quasi-isometrically embedded in Mod(S), then a purely pseudo-Anosov subgroup H <G is convex cocompact in Mod(S) if and only if it is combinatorially quasiconvex in G. We use this criterion to construct convex cocompact subgroups of Mod(S) whose orbit maps into the curve complex have small Lipschitz constants.