Work

Dynamic asymptotic dimension for actions of virtually cyclic groups

Year: 2021

Type: article

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 $C^{*}$ -algebras arising from minimal free $\mathbb {Z}$ -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 Szabó in the metrisable setting.

Source: Proceedings of the Edinburgh Mathematical Society

DOI: 10.1017/s0013091521000183

Authors: Massoud Amini, Kang Li, Damian Sawicki, Ali Shakibazadeh

Institutions: Tarbiat Modares University, Institute of Mathematics, Polish Academy of Sciences, Max Planck Institute for Mathematics

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Max-Planck-Gesellschaft

Award: G5145424685