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Asymptotic dimension of graphs of groups and one-relator groups

Panagiotis Tselekidis

Algebraic & Geometric Topology 23 (2023) 3587–3613
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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