Minimal Dynamical Systems on Connected Odd Dimensional Spaces

Abstract

AbstractLetbe a minimal homeomorphism (n ≥1). We show that the crossed producthas rational tracial rank at most one. Let Ω be a connected, compact, metric space with finite covering dimension and with. Suppose that,where Giis a finite abelian group, i = 0,1. Let β:Ω→Ωbe a minimal homeomorphism. We also show thathas 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.