NUCLEAR DIMENSION AND CLASSIFICATION OF C-ALGEBRAS ASSOCIATED TO SMALE SPACES

NUCLEAR DIMENSION AND CLASSIFICATION OF C-ALGEBRAS ASSOCIATED TO SMALE SPACES

We show that the homoclinic C*-algebras of mixing Smale spaces are classifiable by the Elliott invariant. To obtain this result, we prove that the stable, unstable, and homoclinic C*-algebras associated to such Smale spaces have finite nuclear dimension. Our proof of finite nuclear dimension relies...

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Veröffentlicht in:Transactions of the American Mathematical Society 2018-05, Vol.370 (5), p.3467-3485
Hauptverfasser: DEELEY, ROBIN J., STRUNG, KAREN R.
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description We show that the homoclinic C*-algebras of mixing Smale spaces are classifiable by the Elliott invariant. To obtain this result, we prove that the stable, unstable, and homoclinic C*-algebras associated to such Smale spaces have finite nuclear dimension. Our proof of finite nuclear dimension relies on Guentner, Willett, and Yu’s notion of dynamic asymptotic dimension.
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title NUCLEAR DIMENSION AND CLASSIFICATION OF C-ALGEBRAS ASSOCIATED TO SMALE SPACES
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