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.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7046