K-Homology and Index Theory

Nigel Higson (Penn State University)
Tuesday January 19th, 2010

These talks will be about the C*-algebra approach to index theory and K-theory that was proposed by Atiyah and worked out in detail by Kasparov.

Atiyah pointed out that an elliptic operator on a manifold can be viewed as cycles for the homology theory that is dual to K-theory. This led him to suggest a functional-analytic definition for K-homology, and Kasparov later worked out the complete theory. In the first talk I shall tell more of this story.