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2017 Geometric embedding properties of Bestvina–Brady subgroups
Hung Tran
Algebr. Geom. Topol. 17(4): 2499-2510 (2017). DOI: 10.2140/agt.2017.17.2499

Abstract

We compute the relative divergence of right-angled Artin groups with respect to their Bestvina–Brady subgroups and the subgroup distortion of Bestvina–Brady subgroups. We also show that for each integer n 3, there is a free subgroup of rank n of some right-angled Artin group whose inclusion is not a quasi-isometric embedding. The corollary answers the question of Carr about the minimum rank n such that some right-angled Artin group has a free subgroup of rank n whose inclusion is not a quasi-isometric embedding. It is well known that a right-angled Artin group AΓ is the fundamental group of a graph manifold whenever the defining graph Γ is a tree with at least three vertices. We show that the Bestvina–Brady subgroup HΓ in this case is a horizontal surface subgroup.

Citation

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Hung Tran. "Geometric embedding properties of Bestvina–Brady subgroups." Algebr. Geom. Topol. 17 (4) 2499 - 2510, 2017. https://doi.org/10.2140/agt.2017.17.2499

Information

Received: 23 August 2016; Revised: 20 October 2016; Accepted: 1 January 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06762697
MathSciNet: MR3686403
Digital Object Identifier: 10.2140/agt.2017.17.2499

Subjects:
Primary: 20F65, 20F67
Secondary: 20F36

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 4 • 2017
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