Asymptotic dimension of graphs of groups and one-relator groups

Tselekidis, Panagiotis

doi:10.2140/agt.2023.23.3587

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Asymptotic dimension of graphs of groups and one-relator groups

Panagiotis Tselekidis

Algebraic & Geometric Topology 23 (2023) 3587–3613

DOI: 10.2140/agt.2023.23.3587

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 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.

Keywords

asymptotic dimension, one-relator groups, graph of groups, RAAGs, geometric group theory

Mathematical Subject Classification

Primary: 20E08, 20F65

References

Publication

Received: 3 June 2021

Revised: 11 April 2022

Accepted: 13 July 2022

Published: 5 November 2023

Authors

Panagiotis Tselekidis
Mathematical Institute University of Oxford Oxford United Kingdom

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Volume 23, issue 8 (2023)