Geodesic
Geometric embedding properties of Bestvina–Brady subgroups
Tran, Hung1
1Department of Mathematics, The University of Georgia, Athens, GA, United States
Algebraic and Geometric Topology, Tome 17 (2017) no. 4, pp. 2499-2510
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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.

DOI : 10.2140/agt.2017.17.2499
Classification : 20F65, 20F67, 20F36
Keywords: Bestvina–Brady subgroups, geometric embedding properties, subgroup distortion, relative divergence

Tran, Hung  1

1 Department of Mathematics, The University of Georgia, Athens, GA, United States 
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Tran, Hung. Geometric embedding properties of Bestvina–Brady subgroups. Algebraic and Geometric Topology, Tome 17 (2017) no. 4, pp. 2499-2510. doi: 10.2140/agt.2017.17.2499

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