Minimal Dynamical Systems on Connected Odd Dimensional Spaces

Abstract

AbstractLet be a minimal homeomorphism (n ≥1). We show that the crossed product has rational tracial rank at most one. Let Ω be a connected, compact, metric space with finite covering dimension and with . Suppose that ,where Gi is a finite abelian group, i = 0,1. Let β:Ω→Ωbe a minimal homeomorphism. We also show that has rational tracial rank at most one and is classifiable. In particular, this applies to the minimal dynamical systems on odd dimensional real projective spaces. This is done by studying minimal homeomorphisms on X✗Ω, where X is the Cantor set.