Consider a minimal and free topological dynamical system (X, Zᵈ). It is shown that zero mean dimension of (X, Zᵈ) is characterized by Z-absorption of the crossed product C*-algebra A=C (X) Zᵈ, where Z is the Jiang-Su algebra. In fact, among other conditions, the following are shown to be equivalent: (1) (X, Zᵈ) has the small boundary property. (2) A A Z. (3) A has uniform property. (4) l^ (A) /J₂, , ₓ (₀) has real rank zero. The same statement also holds for unital simple AH algebras with diagonal maps.
Elliott et al. (Fri,) studied this question.
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