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 finitely generated one relator group is at most two, confirming a conjecture of A.Dranishnikov. As further corollaries we calculate the exact asymptotic dimension of Right-angled Artin groups and we give a new upper bound for the asymptotic dimension of fundamental groups of graphs of groups.

31 pages, 7 figures

References in corpus (3)

• Asymptotic dimension in Bedlewo
• Asymptotic dimension of one relator groups
• Assouad-Nagata dimension of finitely generated C'(1/6) groups

Cited by in corpus (2)

• Asymptotic dimension of multi-ended quasi-transitive graphs
• $L^p$ coarse Baum-Connes conjecture via $C_0$ coarse geometry