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

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

2005-08-02

arxiv.org/abs/math/0508057v3

Algebr. Geom. Topol. 6 (2006) 1987-2029

Mathematics

Group Theory

This is the version published by Algebraic & Geometric Topology on 14 November 2006

Scientific paper

10.2140/agt.2006.6.1987

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.

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