Nuclear dimension and classification of 𝐶*-algebras associated to Smale spaces

Abstract

We show that the homoclinic C ∗ \mathrm {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 ∗ \mathrm {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.