Minimal dynamics and the classification of C*-algebras

Let X be an infinite, compact, metrizable space of finite covering dimension and α: X → X a minimal homeomorphism. We prove that the crossed product C(X) ⋊_α &Z; absorbs the Jiang-Su algebra tensorially and has finite nuclear dimension. As a consequence, these algebras are determined up to isomorphism by their graded ordered K-theory under the necessary condition that their projections separate traces. This result applies, in particular, to those crossed products arising from uniquely ergodic homeomorphisms.