Geometric embedding properties of Bestvina–Brady subgroups

Tran, Hung

doi:10.2140/agt.2017.17.2499

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Geometric embedding properties of Bestvina–Brady subgroups

Hung Cong Tran

Algebraic & Geometric Topology 17 (2017) 2499–2510

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 $n \geq 3$ , 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 $A_{Γ}$ 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 $H_{Γ}$ in this case is a horizontal surface subgroup.

Keywords

Bestvina–Brady subgroups, geometric embedding properties, subgroup distortion, relative divergence

Mathematical Subject Classification 2010

Primary: 20F65, 20F67

Secondary: 20F36

References

Publication

Received: 23 August 2016

Revised: 20 October 2016

Accepted: 1 January 2017

Published: 3 August 2017

Authors

Hung Cong Tran
Department of Mathematics The University of Georgia Athens, GA United States

Volume 17, issue 4 (2017)