Minimal Dynamical Systems on Connected Odd Dimensional Spaces

摘要

Let beta:S2n+1 -> S2n+1 be a minimal homeomorphism (n >= 1). We show that the crossed product C(S2n+1) (sic)(beta) Z has rational tracial rank at most one. Let Omega be a connected, compact, metric space with finite covering dimension and with H-1 (Omega, Z) = {0}. Suppose that K-i (C(Omega)) = Z circle plus G(i), where G(i) is a finite abelian group, i = 0,1. Let beta:Omega -> Omega be a minimal homeomorphism. We also show that A = C(Omega) (sic)(beta) Z 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 x Omega, where X is the Cantor set.