A topological proof of K-triviality of flat bundles

Valerio Proietti  (University of Copenhagen)

14:00-16:00, Nov 13, 2018   ÎÄ¸½Â¥206

Abstract:

Given a finitely generated Hilbert module bundle over a compact Hausdorff space, one gets a K-theory class for the algebra of continuous functions on the base with values in the ground C^*-algebra. A topological argument involving the Chern character shows that this class is trivial and this simple fact implies an index theorem in the style of Atiyah's celebrated result on the equality between the ordinary index and the L^2-index.