American Institute of Mathematical Sciences

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

Research announcement: The structure of groups with a quasiconvex hierarchy

Daniel T. Wise 1,

1. 

Dept. of Math. & Stats., McGill University, Montreal, QC, Canada

Received  August 2009 Revised  September 2009 Published  October 2009

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, 3-manifold, subgroup separable, one-relator group..
Mathematics Subject Classification: 53C23, 20F36, 20F55, 20F67, 20F65, 20E2.
Citation: Daniel T. Wise. Research announcement: The structure of groups with a quasiconvex hierarchy. Electronic Research Announcements, 2009, 16: 44-55. doi: 10.3934/era.2009.16.44
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