Volume 8, issue 4 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Angle-deformations in Coxeter groups

Timothée Marquis and Bernhard Mühlherr

Algebraic & Geometric Topology 8 (2008) 2175–2208
Abstract

The isomorphism problem for Coxeter groups has been reduced to its “reflection preserving version” by B Howlett and the second author. Thus, in order to solve it, it suffices to determine for a given Coxeter system (W,R) all Coxeter generating sets S of W which are contained in RW, the set of reflections of (W,R). In this paper, we provide a further reduction: it suffices to determine all Coxeter generating sets S RW which are sharp-angled with respect to R.

Added 22 May 2012: The description of Figure 3 in Section 8.1 has been corrected.

Keywords
angle-deformation, Coxeter group, isomorphism problem, sharp-angled
Mathematical Subject Classification 2000
Primary: 20F55
Secondary: 51F15
References
Publication
Received: 21 February 2008
Revised: 19 October 2008
Accepted: 29 October 2008
Published: 3 December 2008
Corrected: 22 May 2012
Authors
Timothée Marquis
Université Libre de Bruxelles
Département de Mathématiques
Boulevard du Triomphe CP 216
Brussels, 1050
Belgium
Bernhard Mühlherr
Universität Giessen
Mathematisches Institut
Arndtstrasse 2
Giessen, D-35392
Germany