Proceedings of the Edinburgh Mathematical Society ( IF 0.512 ) Pub Date : 2021-05-04 , DOI: 10.1017/s0013091521000183
Massoud Amini, Kang Li, Damian Sawicki, Ali Shakibazadeh

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.

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