The C*-algebra of a minimal homeomorphism of zero mean dimension

Let $X$ be an infinite compact metrizable space, and let $\sigma :X\to X$ be a minimal homeomorphism. Suppose that $(X,\sigma )$ has zero mean topological dimension. The associated C*-algebra $A=\mathrm{C}(X){⋊}_{\sigma }\mathbb{Z}$ is shown to absorb the Jiang-Su algebra $\mathcal{Z}$ tensorially, i.e., $A\cong A\otimes\mathcal Z$\mathrm{.}Thisimpliesthat$A$isclassifiablewhen$(X, \sigma)$ is uniquely ergodic. Moreover, without any assumption on the mean dimension, it is shown that $A\otimes A$ always absorbs the Jiang-Su algebra.