Nuclear dimension and classification of C*-algebras associated to Smale spaces
arXiv:1601.02432
Abstract
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.
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