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arXiv · 1410.4589

Recognizing Right-Angled Coxeter Groups Using Involutions

Charles Cunningham·Andy Eisenberg·Adam Piggott·Kim Ruane
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Abstract

We consider the question of determining whether a given group (especially one generated by involutions) is a right-angled Coxeter group. We describe a group invariant, the involution graph, and we characterize the involution graphs of right-angled Coxeter groups. We use this characterization to describe a process for constructing candidate right-angled Coxeter presentations for a given group or proving that one cannot exist. We provide some first applications. In addition, we provide an elementary proof of rigidity of the defining graph for a right-angled Coxeter group. We also recover a result stating that if the defining graph contains no SILs, then Aut^0(W) is a right-angled Coxeter group.

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Charles Cunningham, Andy Eisenberg, Adam Piggott, Kim Ruane. 2014-10-16. Recognizing Right-Angled Coxeter Groups Using Involutions. https://doi.org/10.2140/pjm.2016.284.41

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