Some applications of K-homology

Nigel Higson (Penn State University)
Tuesday January 26th, 2010 RLM 9.166

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.

What is K-homology good for? I'll try to answer with examples in this and the previous talks. There is an obvious connection to the Atiyah-Singer index theorem, and roughly speaking K-homology provides a context in which to consider the index theorem's many elaborations. A general theme is that while two operators may look rather different, for example when studied using a symbol calculus, functional analysis and the framework of K-homology can sometimes give a means to identify their Fredholm index theories