Algebraic & Geometric Topology

Angle-deformations in Coxeter groups

Timothée Marquis and Bernhard Mühlherr

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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 SRW 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

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

Received: 21 February 2008
Revised: 19 October 2008
Accepted: 29 October 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Secondary: 51F15: Reflection groups, reflection geometries [See also 20H10, 20H15; for Coxeter groups, see 20F55]

angle-deformation Coxeter group isomorphism problem sharp-angled


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.

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