Research announcement: The structure of groups with a quasiconvex hierarchy

Daniel Wise
2009 Electronic Research Announcements in Mathematical Sciences  
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.
doi:10.3934/era.2009.16.44 fatcat:zhftsdi2wjf7vhwnilfasj6l5a