Research announcement: The structure of groups with a quasiconvex hierarchy
Daniel T. Wise - Dept. of Math. & Stats., McGill University, Montreal, QC, Canada (email)
Abstract: Let $G$ be a word-hyperbolic group with a quasiconvex hierarchy. We show that $G$ has a finite index subgroup $G'$ that embeds as a quasiconvex subgroup of a right-angled Artin group. It follows that every quasiconvex subgroup of $G$ is a virtual retract, and is hence separable. The results are applied to certain 3-manifold and one-relator groups.
Keywords: CAT(0) cube complex, right-angled artin group, subgroup
separable, 3-manifold, one-relator group.
Received: August 2009; Revised: September 2009; Available Online: October 2009.