Generalizing the Freed-Melrose index theorem
Speaker:
Robin Deeley, University of Hawaii
Date and Time:
Monday, August 22, 2016 - 11:30am to 12:30pm
Location:
Fields Institute, Stewart Library
Abstract:
The index of the Dirac operator on a manifold with boundary with Atiyah-Patodi-Singer boundary conditions is not a topological invariant. In contrast, the Freed-Melrose index theorem provides a topological formula for the mod k reduction of the index of the Dirac operator on a z/k-manifold with Atiyah-Patodi-Singer boundary conditions. I will discuss generalizations of the Freed-Melrose index theorem to manifolds with Baas-Sullivan singularities. These generalizations fit within both geometric K-homology and KK-theory. In regard to the latter, Hilsum's notion of bordism in unbounded KK-theory plays a key role. No knowledge of z/k-manifolds or the Freed-Melrose index theorem will be assumed.
Coauthors: Magnus Goffeng and Bram Mesland