Chern-Simons, Differential K-Theory and Operator Theory

Differential K-theory unites K-theory and differential forms. It has generators given by vector bundles with connection and differential forms; the relations involve Chern-Simons forms. For various reasons, one would like to extend the vector bundles to Hilbert bundles. I'll describe how this can be done. Some operator theoretic issues arise. This is joint work with Alexander Gorokhovsky.