Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls

Let (W,S) be a Coxeter system of finite rank (ie |S| is finite) and let A be the associated Coxeter (or Davis) complex. We study chains of pairwise parallel walls in A using Tits' bilinear form associated to the standard root system of (W,S). As an application, we prove the strong parallel wall conjecture of G Niblo and L Reeves [J Group Theory 6 (2003) 399--413]. This allows to prove finiteness of the number of conjugacy classes of certain one-ended subgroups of W, which yields in turn the determination of all co-Hopfian Coxeter groups of 2--spherical type.Comment: This is the version published by Algebraic & Geometric Topology on 14 November 200

A construction of hyperbolic Coxeter groups

We give a simple construction of Gromov hyperbolic Coxeter groups of arbitrarily large virtual cohomological dimension. Our construction provides new examples of such groups. Using this one can construct e.g. new groups having some interesting asphericity properties.Comment: 14 page