Volume 17, issue 4 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Geometric embedding properties of Bestvina–Brady subgroups

Hung Cong Tran

Algebraic & Geometric Topology 17 (2017) 2499–2510

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.

Bestvina–Brady subgroups, geometric embedding properties, subgroup distortion, relative divergence
Mathematical Subject Classification 2010
Primary: 20F65, 20F67
Secondary: 20F36
Received: 23 August 2016
Revised: 20 October 2016
Accepted: 1 January 2017
Published: 3 August 2017
Hung Cong Tran
Department of Mathematics
The University of Georgia
Athens, GA
United States