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.
- Pub Date:
- January 2016
- Mathematics - Operator Algebras;
- Mathematics - Dynamical Systems
- 19 pages. Minor typos fixed, reference added. To appear in Trans. Amer. Math. Soc. Only changes in version 3 are to KS's grant information