Asymptotic Dimension of Graphs of Groups and One Relator Groups

TL;DR

This paper establishes new bounds on the asymptotic dimension of various groups, including one relator groups and right-angled Artin groups, advancing understanding of their geometric properties.

Contribution

It proves a new inequality for asymptotic dimension of HNN-extensions and confirms a conjecture that one relator groups have asymptotic dimension at most two.

Findings

Asymptotic dimension of one relator groups is at most two.

Exact asymptotic dimension of right-angled Artin groups is calculated.

New upper bounds for fundamental groups of graphs of 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.