Research announcement: The structure of groups with a quasiconvex hierarchy

Daniel T. Wise

doi:10.3934/era.2009.16.44

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

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Research announcement: The structure of groups with a quasiconvex hierarchy

Daniel T. Wise^1,

1.
Dept. of Math. & Stats., McGill University, Montreal, QC

Received: July 31, 2009

Revised: August 31, 2009

Published: December 2008

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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.

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

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