Characterizing divergence and thickness in right-angled Coxeter groups
Geometric Topology
2022-08-16 v3 Group Theory
Abstract
We completely classify the possible divergence functions for right-angled Coxeter groups (RACGs). In particular, we show that the divergence of any such group is either polynomial, exponential or infinite. We prove that a RACG is strongly thick of order k if and only if its divergence function is a polynomial of degree k+1. Moreover, we show that the exact divergence function of a RACG can easily be computed from its defining graph by an invariant we call the hypergraph index.
Keywords
Cite
@article{arxiv.2007.13796,
title = {Characterizing divergence and thickness in right-angled Coxeter groups},
author = {Ivan Levcovitz},
journal= {arXiv preprint arXiv:2007.13796},
year = {2022}
}
Comments
Accepted for publication by the Journal of Topology. Incorporated referee's comments and added many more figures