## Algebraic & Geometric Topology

### Angle-deformations in Coxeter groups

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 8, Number 4 (2008), 2175-2208.

Dates
Revised: 19 October 2008
Accepted: 29 October 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796931

Digital Object Identifier
doi:10.2140/agt.2008.8.2175

Mathematical Reviews number (MathSciNet)
MR2465738

Zentralblatt MATH identifier
1184.20032

#### Citation

Marquis, Timothée; Mühlherr, Bernhard. Angle-deformations in Coxeter groups. Algebr. Geom. Topol. 8 (2008), no. 4, 2175--2208. doi:10.2140/agt.2008.8.2175. https://projecteuclid.org/euclid.agt/1513796931

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