Young Mathematicians in C*-Algebras
Secondary invariants of elliptic operators (Guoliang Yu)
In my mini-course, I will introduce the concept of secondary invariants of elliptic operators and discuss their applications to geometry and topology. The secondary invariants are defined when the elliptic operators are invertible and therefore their primary index theoretic invariants vanish. The secondary invariants live in the K-theory of certain C* algebras and serve as obstructions for the inverses of the elliptic operators to be local.
I will apply the secondary invariants to measure the degree of non-rigidity of topological manifolds and the size of moduli spaces of positive scalar curvature metrics.