Dynamical complexity and K-theory of Lp operator crossed products

Abstract

We apply quantitative (or controlled) [Formula: see text]-theory to prove that a certain [Formula: see text] assembly map is an isomorphism for [Formula: see text] when an action of a countable discrete group [Formula: see text] on a compact Hausdorff space [Formula: see text] has finite dynamical complexity. When [Formula: see text], this is a model for the Baum–Connes assembly map for [Formula: see text] with coefficients in [Formula: see text], and was shown to be an isomorphism by Guentner et al.