Bordism extensions and the Callias index theorem

Hitoshi Moriyoshi  (Nagoya University)

14:00 pm - 15:00 pm, May 11th, 2016   Science Building A1510

Abstract:

The Hopf-Wiener extension is a Toeplitz type extension of the group $C^*$-algebra for the real numbers. It is also constructed from a bordism with cylindrical end, namely, compact manifold with a half-cylinder attached to the boundary. On such a manifold we can develop the Callias index theorem for the Dirac operator with a suitable potential. I shall talk about the relation between the Callias index and the connection map in the 6-term exact sequence of $K$-theory from the bordism extension.