Volume 6, issue 2 (2006)

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

Volume 16
Issue 4, 1827–2458
Issue 3, 1253–1825
Issue 2, 621–1251
Issue 1, 1–620

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
Commensurability and separability of quasiconvex subgroups

Frédéric Haglund

Algebraic & Geometric Topology 6 (2006) 949–1024

arXiv: 0904.2698


We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph product of finite groups, a uniform lattice is commensurable with the graph product provided all of its quasiconvex subgroups are separable. We obtain a similar result for uniform lattices of the Davis complex of Gromov-hyperbolic two-dimensional Coxeter groups. We also prove that every extension of a uniform lattice of a CAT(0) square complex by a finite group is virtually trivial, provided each quasiconvex subgroup of the lattice is separable.

graph products, Coxeter groups, commensurability, separability, quasiconvex subgroups, right-angled buildings, Davis' complexes, finite extensions
Mathematical Subject Classification 2000
Primary: 20F55, 20F67, 20F65
Secondary: 20E26, 51E24, 20E22, 20J06
Forward citations
Received: 25 July 2005
Accepted: 23 November 2005
Published: 9 August 2006
Frédéric Haglund
Laboratoire de Mathématiques
Université de Paris XI (Paris-Sud)
91405 Orsay