A new upper bound for the Asymptotic Dimension of RACGs

Abstract

Abstract Let $W_{\Gamma} $ be the right-angled Coxeter group with defining graph $\Gamma $ . We show that the asymptotic dimension of $W_{\Gamma} $ is smaller than or equal to $\mathrm{dim}_{CC}(\Gamma )$ , the clique-connected dimension of the graph. We generalize this result to graph products of finite groups.