Recognizing Right-Angled Coxeter Groups Using Involutions
Group Theory
2016-08-03 v2 Combinatorics
Geometric Topology
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.
Cite
@article{arxiv.1410.4589,
title = {Recognizing Right-Angled Coxeter Groups Using Involutions},
author = {Charles Cunningham and Andy Eisenberg and Adam Piggott and Kim Ruane},
journal= {arXiv preprint arXiv:1410.4589},
year = {2016}
}
Comments
43 pages, 13 figures