K-Theoretic Duality for Shifts of Finite Type

We will study the stable and unstable Ruelle algebras associated to a hyperbolic homeomorphism of a compact space. To do this, we will describe a notion of K-theoretic duality for -algebras which generalizes Spanier-Whitehead duality in topology. A criterion for checking that it holds is presented. As an application it is shown that the Ruelle algebras which are associated to subshifts of finite type, (and agree with Cuntz-Krieger algebras in this case) satisfy this criterion and hence are dual. Received: 23 February 1996 / Accepted: 10 December