Commensurability and separability of quasiconvex subgroups

Haglund, Frédéric¹

¹Laboratoire de Mathématiques, Université de Paris XI (Paris-Sud), 91405 Orsay, France

Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 949-1024

Résumé

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.

Détail

DOI : 10.2140/agt.2006.6.949

Keywords: graph products, Coxeter groups, commensurability, separability, quasiconvex subgroups, right-angled buildings, Davis' complexes, finite extensions

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