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

Caprace, Pierre-Emmanuel
(2006) Algebraic & Geometric Topology — Vol. 6, p. 1987-2029 (2006)

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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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Caprace, P.-E. (2006). Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls. Algebraic & Geometric Topology, 6, 1987-2029. https://doi.org/10.2140/agt.2006.6.1987 (Original work published 2006)