Peter Hochs (Radboud)
For many classical, numerical invariants of manifolds, there are `higher’ versions, defined in terms of the action by the fundamental group of a given manifold on its universal cover. These generally capture more, or at least different information than their classical counterparts. For index-theoretic invariants, such higher versions often lie in the K-theory of the C*-algebra of the fundamental group of the manifold.
With my PhD student Aquerman Yanes, we constructed such a higher, K-theoretic version of spectral flow of families of Dirac operators on compact manifolds, and studied its properties. A central result is a higher version of the classical Robbin-Salomon `index = spectral flow' equality. The talk will be aimed at people who are not necessarily familiar with C*-algebras and K-theory.
