Algebraic & Geometric Topology 8 (2008) 2175–2208

DOI: 10.2140/agt.2008.8.2175

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 R^W, the set of reflections of (W,R). In this paper, we provide a further reduction: it suffices to determine all Coxeter generating sets S ⊆ 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

Mathematical Subject Classification

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