Commensurability and separability of quasiconvex subgroups

Haglund, Frédéric

doi:10.2140/agt.2006.6.949

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

Commensurability and separability of quasiconvex subgroups

Frédéric Haglund

Algebraic & Geometric Topology 6 (2006) 949–1024

DOI: 10.2140/agt.2006.6.949

arXiv: 0904.2698

Abstract

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 $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo class="qopname"> CAT</mo><mrow><mo class="MathClass-open">(</mo><mrow><mn>0</mn></mrow><mo class="MathClass-close">)</mo></mrow></math>$ square complex by a finite group is virtually trivial, provided each quasiconvex subgroup of the lattice is separable.

Keywords

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

References

Forward citations

Publication

Received: 25 July 2005

Accepted: 23 November 2005

Published: 9 August 2006

Authors

Frédéric Haglund
Laboratoire de Mathématiques Université de Paris XI (Paris-Sud) 91405 Orsay France

Volume 6, issue 2 (2006)