Cyclic cohomology and minimal diffeomorphisms

Hongzhi Liu  (Fudan University)

10:00-11:00 am, October 12th, 2016   Science Building A1510

Abstract:

$\alpha_n (n>0)$ are minimal unique ergodic diffeomorphisms of odd dimensional spheres $S^{2n+1}$. The $C^*$ crossed product algebras $C(S^{2n+1})\rtimes_{\alpha_n} \mathbb{Z}$ are isomorphic to each other for any $n>0$. However we can differ their dense subalgebras, smooth crossed product algebras $C^{\infty}(S^{2n+1})\rtimes_{\alpha_n} \mathbb{Z}$, by the grading structure of their cyclic cohomology. Furthermore, we construct two minimal unique ergodic diffeomorphisms of the same manifolds which give the same $C^*$ crossed product algebra and different smooth crossed product algebras. We show this also by computing the grading structure of their cyclic cohomology.