Mathematics – Group Theory
Scientific paper
2005-08-02
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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