Elementary amenability and almost finiteness

Abstract

We show that every free continuous action of a countably infinite elementary amenable group on a finite-dimensional compact metrizable space is almost finite. As a consequence, the crossed products of minimal such actions are $\mathcal{Z}$-stable and classified by their Elliott invariant.

17 pages, main argument corrected and simplified

References in corpus (7)

• Nuclear dimension of simple C*-algebras
• Classification of finite simple amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras
• Folner tilings for actions of amenable groups
• The comparison property of amenable groups
• Symbolic extensions of amenable group actions and the comparison property
• Comparison radius and mean topological dimension: ${\mathbb{Z}}^d$-actions
• Minimal dynamics and Z-stable classification