Speaker: N. Christopher Phillips (Univ. Oregon)

Title: Strict comparison for crossed products by free minimal actions of Z^d

Abstract: Let X be a compact manifold, and let h be a smooth free minimal action of Z^d on X. Then C^*(Z^d, X, h) has strict comparison of positive elements. That is, the order on the Cuntz semigroup is essentially determined by the dimension functions coming from traces. It follows that the order on projections over C^*(Z^d, X, h) is determined by traces in the sense of Blackadar. We will describe, in particular, the construction of a "large" subalgebra of the crossed product, which plays a role similar to that of the Putnam subalgebra C^*(Z, X, h)_y for a minimal homeomorphism h of a compact metric space X and a point y in X.