Volume 10, issue 3 (2010)

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

Volume 24
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

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
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
Relative hyperbolicity and relative quasiconvexity for countable groups

G Christopher Hruska

Algebraic & Geometric Topology 10 (2010) 1807–1856
Abstract

We lay the foundations for the study of relatively quasiconvex subgroups of relatively hyperbolic groups. These foundations require that we first work out a coherent theory of countable relatively hyperbolic groups (not necessarily finitely generated). We prove the equivalence of Gromov, Osin and Bowditch’s definitions of relative hyperbolicity for countable groups.

We then give several equivalent definitions of relatively quasiconvex subgroups in terms of various natural geometries on a relatively hyperbolic group. We show that each relatively quasiconvex subgroup is itself relatively hyperbolic, and that the intersection of two relatively quasiconvex subgroups is again relatively quasiconvex. In the finitely generated case, we prove that every undistorted subgroup is relatively quasiconvex, and we compute the distortion of a finitely generated relatively quasiconvex subgroup.

Keywords
relative hyperbolicity, quasiconvex
Mathematical Subject Classification 2000
Primary: 20F65, 20F67
References
Publication
Received: 16 April 2009
Revised: 24 April 2010
Accepted: 10 May 2010
Published: 3 September 2010
Authors
G Christopher Hruska
Department of Mathematical Sciences
University of Wisconsin–Milwaukee
PO Box 413
Milwaukee, WI 53201
USA
http://www.uwm.edu/~chruska