Dynamic asymptotic dimension for actions of virtually cyclic groups
Amini M, Li K, Sawicki D, Shakibazadeh A (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 64
Pages Range: 364-372
Journal Issue: 2
DOI: 10.1017/S0013091521000183
Abstract
We show that the dynamic asymptotic dimension of an action of an infinite virtually cyclic group on a compact Hausdorff space is always one if the action has the marker property. This in particular covers a well-known result of Guentner, Willett, and Yu for minimal free actions of infinite cyclic groups. As a direct consequence, we substantially extend a famous result by Toms and Winter on the nuclear dimension of -algebras arising from minimal free -actions. Moreover, we also prove the marker property for all free actions of countable groups on finite-dimensional compact Hausdorff spaces, generalizing a result of Szabo in the metrisable setting.
Authors with CRIS profile
Involved external institutions
Tarbiat Modares University
Iran, Islamic Republic of (IR)
Max-Planck-Institut für Mathematik (MPIM)
Germany (DE)
Mathematical Institute of the Polish Academy of Sciences
Poland (PL)
Iran, Islamic Republic of (IR)
Max-Planck-Institut für Mathematik (MPIM)
Germany (DE)
Mathematical Institute of the Polish Academy of Sciences
Poland (PL)
How to cite
APA:
Amini, M., Li, K., Sawicki, D., & Shakibazadeh, A. (2021). Dynamic asymptotic dimension for actions of virtually cyclic groups. Proceedings of the Edinburgh Mathematical Society, 64(2), 364-372. https://dx.doi.org/10.1017/S0013091521000183
MLA:
Amini, Massoud, et al. "Dynamic asymptotic dimension for actions of virtually cyclic groups." Proceedings of the Edinburgh Mathematical Society 64.2 (2021): 364-372.
BibTeX: Download