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2006 Conjugacy of $2$–spherical subgroups of Coxeter groups and parallel walls
Pierre-Emmanuel Caprace
Algebr. Geom. Topol. 6(4): 1987-2029 (2006). DOI: 10.2140/agt.2006.6.1987

Abstract

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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Pierre-Emmanuel Caprace. "Conjugacy of $2$–spherical subgroups of Coxeter groups and parallel walls." Algebr. Geom. Topol. 6 (4) 1987 - 2029, 2006. https://doi.org/10.2140/agt.2006.6.1987

Information

Received: 2 August 2005; Revised: 31 August 2006; Accepted: 4 October 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1160.20031
MathSciNet: MR2263057
Digital Object Identifier: 10.2140/agt.2006.6.1987

Subjects:
Primary: 20F5
Secondary: 20F65, 20F67, 51F15

Rights: Copyright © 2006 Mathematical Sciences Publishers

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