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Minimal Dynamics and K-Theoretic Rigidity: Elliott’s Conjecture

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Abstract

Let X be a compact infinite metric space of finite covering dimension and α : X → X a minimal homeomorphism. We prove that the crossed product \({\mathcal{C}(X) \rtimes_\alpha \mathbb{Z}}\) 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.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN, 47906, USA

    Andrew S. Toms

  2. Department of Mathematics, University of Muenster, Einsteinstrasse 62, 48149, Muenster, Germany

    Wilhelm Winter

Authors
  1. Andrew S. Toms
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  2. Wilhelm Winter
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Correspondence to Andrew S. Toms.

Additional information

Supported by: EPSRC First Grant EP/G014019/1 and by an NSERC Discovery Grant.

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Toms, A.S., Winter, W. Minimal Dynamics and K-Theoretic Rigidity: Elliott’s Conjecture. Geom. Funct. Anal. 23, 467–481 (2013). https://doi.org/10.1007/s00039-012-0208-1

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  • DOI: https://doi.org/10.1007/s00039-012-0208-1

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