Abstract
The paper considers a mixing Smale space, the relations of stable and unstable equivalence on such a space and the C *-algebras which are constructed from them. In general, these associations are not functorial. However, it is shown that, if one restricts to the class of s-resolving, finite-to-one factor maps, then the construction of the stable C *-algebra is contravariant, while that of the unstable C *-algebra is covariant. The paper also discusses the constructions of these C *-algebras for Smale spaces which are not mixing.
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