Asymptotic dimension of graphs of groups and one-relator groups

Abstract

We prove a new inequality for the asymptotic dimension of HNN-extensions. We deduce that the asymptotic dimension of every one relator group is at most two, confirming a conjecture of A.Dranishnikov. As another corollary we calculate the exact asymptotic dimension of Right-angled Artin groups. We prove a new upper bound for the asymptotic dimension of fundamental groups of graphs of groups. This leads to a partial result on the asymptotic Morita conjecture for finitely generated groups.