#### Volume 8, issue 4 (2008)

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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 $\left(W,R\right)$ all Coxeter generating sets $S$ of $W$ which are contained in ${R}^{W}$, the set of reflections of $\left(W,R\right)$. In this paper, we provide a further reduction: it suffices to determine all Coxeter generating sets $S\subseteq {R}^{W}$ 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
Primary: 20F55
Secondary: 51F15