Eigenvalues, K-theory and Minimal Flows

Let (Y, T) be a minimal suspension flow built over a dynamical system (X, S) and with (strictly positive, continuous) ceiling function f : X → ℝ. We show that the eigenvalues of (Y, T) are contained in the range of a trace on the K0-group of (X, S). Moreover, a trace gives an order isomorphism of a subgroup of K0(C(X) ⋊Sℤ) with the group of eigenvalues of (Y, T). Using this result, we relate the values of t for which the time-t map on the minimal suspension flow is minimal with the K-theory of the base of this suspension.