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

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Caprace, Pierre-Emmanuel [UCL]

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.

Document type Article de périodique (Journal article)
Publication date 2006
Language Anglais
Journal information "Algebraic & Geometric Topology" - Vol. 6, p. 1987-2029 (2006)
Peer reviewed yes
Publisher University of Warwick ((United Kingdom) [S.l.])
issn 1472-2747
e-issn 1472-2739
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Links
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Bibliographic reference Caprace, Pierre-Emmanuel. Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls. In: Algebraic & Geometric Topology, Vol. 6, p. 1987-2029 (2006)
Permanent URL http://hdl.handle.net/2078.1/94638