Mühlherr's twist conjecture for finite-rank Coxeter systems
Mühlherr's twist conjecture for finite-rank Coxeter systems
Let be a Coxeter system of finite rank, and let be another set of Coxeter generators of . Define
The set is sharp-angled with respect to if, for each pair such that , there is a such that . The Coxeter systems and are twist equivalent if there is a finite sequence of elementary twists transforming into .
Twist conjecture. If and is sharp-angled with respect to , then is twist equivalent to .
This conjecture concerns the isomorphism problem for finite-rank Coxeter systems and predicts that the stated inclusion and sharp-angledness conditions are sufficient for the two generating sets to be related by elementary twists. It is attributed to Mühlherr; the supplied source gives no resolution, so its status remains open.
Sources & referencesView supporting material
Primary source
John Ratcliffe and Steven Tschantz, “JSJ decompositions of Coxeter groups over FA subgroups”, arXiv:0910.5732 (2009).
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