Comparison Theory and Smooth Minimal C * -dynamics

  title={Comparison Theory and Smooth Minimal C * -dynamics},
  author={Andrew S. Toms}
We prove that the C *-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of countably generated Hilbert modules over such algebras, and to a similar classification for the closures of unitary orbits of self-adjoint elements. We also obtain a structure theorem for the Cuntz semigroup in this setting, and prove a conjecture of Blackadar and… CONTINUE READING