Separating quasiconvex subgroups of right-angled Artin groups

A graph group, or right-angled Artin group, is a group given by a presentation where the only relators are commutators of the generators. A graph group presentation corresponds in a natural way to a simplicial graph, with each generator corresponding to a vertex, and each commutator relator corresponding to an edge. Suppose that G is a graph group whose corresponding graph is a tree and H is a subgroup of G. We show that if H is quasiconvex with respect to either the word metric on G or the CAT(0) metric on the universal cover of the standard complex for G, then H is separable, that is, H is the intersection of finite index subgroups of G. We also discuss some consequences relating to certain 3-manifold groups. Received: 19 July 2000; in final form: 2 March 2001 / Published online: 29 April 2002