The cohomology and K-theory of commuting hemeomorphisms of the Cantor set

Given a Z(d) homeomorphic action, cu, on the Canter set, X, we consider the higher order continuous integer valued dynamical cohomology, H*(X, alpha). We also consider the dynamical K-theory of the action, the K-theory of the crossed product C*-algebra C(X) x(alpha) Z(d). We show that these two invariants are essentially equivalent. We also show that they only take torsion free values. Our work links the two invariants via a third invariant which is based on topological complex K-theory evaluated an an associated mapping torus.