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

Let X be an infinite metrizable compact space, and let σ:X→X be a minimal homeomorphism. Suppose that (X,σ) has zero mean topological dimension. The associated C∗-algebra A=C(X)⋊σZ is shown to absorb the Jiang–Su algebra Z tensorially; that is, A≅A⊗Z. This implies that A is classifiable when (X,σ) is uniquely ergodic. Moreover, without any assumption on the mean dimension, it is shown that A⊗A always absorbs the Jiang–Su algebra.