Minimal dynamical systems on odd dimensional connected spaces

Huaxin Lin  (University of Oregon)

14:00 pm to 15:00 pm, Apr 14th, 2014   Science Building A1510

Abstract:

Let $\alpha \colon S^{2n+1} \to S^{2n+1}$ be a minimal homeomorphism ($n \ge 1$). We show that the crossed product $C(S^{2n+1})\rtimes_\alpha \mathbb{Z}$ has rational tracial rank at most one. Let $\Omega$ be a connected compact metric space with finite covering dimension and with $H^1(\Omega, \mathbb{Z})=\{ 0 \}.$ Suppose that $K_0(C(\Omega))=\mathbb{Z} \oplus G_0$ and $K_1(C(\Omega))=\mathbb{Z} \oplus G_1,$ where $G_0$ and $G_1$ are finite abelian groups. Let $\beta: \Omega \to \Omega$ be a minimal homeomorphism. We also show that $A=C(\Omega) \rtimes_\beta \mathbb{Z}$ has rational tracial rank at most one and is ${\cal A}.$ In particular, this applies to the minimal dynamical systems on odd dimensional real projective spaces.