Theoretical Statistics and Mathematics Unit, ISI Delhi
The development of K-theory and K-homology- its dual theory- are an integral part of this story and lead Baum and Connes to formulate their conjecture, which can be seen as a far-reaching generalization of the Atiyah-Singer index theorem and has several important consequences in analysis and geometric topology, most notably the Novikov conjecture.
In this talk, we shall describe both these theories and investigate how they are related, in particular through the so-called rho-invariants.