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arXiv · 0903.4133

Minimal Dynamics and K-theoretic Rigidity: Elliott's Conjecture

Andrew S. Toms·Wilhelm Winter
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Abstract

Let X be an infinite, compact, metrizable space of finite covering dimension and h a minimal homeomorphism of X. We prove that the crossed product of C(X) by h 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.

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Andrew S. Toms, Wilhelm Winter. 2009-03-24. Minimal Dynamics and K-theoretic Rigidity: Elliott's Conjecture. https://arxiv.org/abs/0903.4133

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