Examples of different minimal diffeomorphisms giving the same C*-algebras

Abstract

We give examples of minimal diffeomorphisms of compact connected manifolds which are not topologically orbit equivalent, but whose transformation group C*-algebras are isomorphic. The examples show that the following properties of a minimal diffeomorphism are not invariants of the transformation group C*-algebra: having topologically quasidiscrete spectrum; the action on singular cohomology (when the manifolds are diffeomorphic); the homotopy type of the manifold (when the manifolds have the same dimension); and the dimension of the manifold. These examples also give examples of nonconjugate isomorphic Cartan subalgebras, and of nonisomorphic Cartan subalgebras, of simple separable nuclear unital C*-algebras with tracial rank zero and satisfying the Universal Coefficient Theorem.