Operator Algebra seminar

Speaker:  Rudolf Zeidler (Göttingen)

Title: Secondary coarse index theory and positive scalar curvature

Abstract:  We discuss secondary invariants such as the higher $\rho$-invariant in the context of coarse index theory and positive scalar curvature (psc). These secondary invariants allow to distinguish complete metrics of psc on spin manifolds up to concordance relative to certain subsets.
Our approach features a new construction of the higher $\rho$-invariant that allows simple proofs of product formulas by utilizing Yu’s localization algebras together with Trout’s spectral picture of K-theory for graded C*-algebras. As an application, we present refined versions of the secondary partitioned manifold index theorem and the delocalized APS index theorem of Piazza-Schick. Moreover, we explain how to use our techniques to obtain new examples of metrics of psc that can be distinguished using the higher $\rho$-invariant.