Commensurability and separability of quasiconvex subgroups

Details Commensurability and separability of quasiconvex subgroups Commensurability and separability of quasiconvex subgroups

2009-04-17

arxiv.org/abs/0904.2698v1

Algebr. Geom. Topol. 6 (2006) 949-1024

Mathematics

Group Theory

This is the version published by Algebraic & Geometric Topology on 9 August 2006

Scientific paper

10.2140/agt.2006.6.949

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.

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