Characterizing divergence and thickness in right-angled Coxeter groups

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.