On asymptotic dimension of amalgamated products and right-angled Coxeter groups

Abstract

We prove that the asymptotic dimension of $A$ and $B$ amalgamated over $C$ is bounded above by the maximum of the asymptotic dimensions of $A$, $B$ and $C+1$. Then we apply this inequality to show that the asymptotic dimension of any right-angled Coxeter group does not exceed the dimension of its Davis complex.