Electronic Research Announcements in Mathematical Sciences (ERA-MS)

Research announcement: The structure of groups with a quasiconvex hierarchy

Pages: 44 - 55, Volume 16, 2009      doi:10.3934/era.2009.16.44

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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.
Mathematics Subject Classification:  53C23, 20F36, 20F55, 20F67, 20F65, 20E26.

Received: August 2009;      Revised: September 2009;      Available Online: October 2009.