Hilbert $C^*$-bundles and Thom isomorphism

10:00 am to 11:00 am, May 20th, 2014   Science Building A1510

Abstract:

In this report, the $K$-groups of $C_0(X,A)$ (where $X$ is a locally compact space and $A$ is a $C^*$-algebra) is shown to be the container of the indices of elliptic morphisms of Hilbert $C^*$-bundles and the Euler characteristic classes of $C^*$-bundle complexes, and a Thom isomorphism is established between $K$-groups of $C_0(X,A)$ and $C_0(V,A)$, where $V \to X$ is a complex vector bundle.