Dynamic asymptotic dimension for actions of virtually cyclic groups
Dynamical Systems
2023-06-22 v3 Group Theory
Operator Algebras
Abstract
We show that the dynamic asymptotic dimension of a minimal free action of an infinite virtually cyclic group on a compact Hausdorff space is always one. This extends a well-known result of Guentner, Willett, and Yu for minimal free actions of infinite cyclic groups. Furthermore, the minimality assumption can be replaced by the marker property, and we prove the marker property for all free actions of countable groups on finite dimensional compact Hausdorff spaces, generalising a result of Szabo in the metrisable setting.
Keywords
Cite
@article{arxiv.2007.00960,
title = {Dynamic asymptotic dimension for actions of virtually cyclic groups},
author = {Massoud Amini and Kang Li and Damian Sawicki and Ali Shakibazadeh},
journal= {arXiv preprint arXiv:2007.00960},
year = {2023}
}
Comments
To appear in Proc. Edinburgh Math. Soc. (2021)