26.04.2024, 15:00
– 2.09.0.14
Forschungsseminar: Gruppen und Operatoralgebren
Properties of affine cellular algebras
Christian Lomp (University of Porto)
Maxim Braverman (Northeastern University)
We show that the (graded) spectral flow of a family of Toeplitz operators on a complete Riemannian manifold is equal to the index of a certain Callias-type operator. When the dimension of the manifold is even this leads to a cohomological formula for the spectral flow.
As an application, we compute the spectral flow of a family of Toeplitz operators on a strongly pseudoconvex domain. This result is similar to the Boutet de Monvel's computation of the index of a single Toeplitz operator on a strongly pseudoconvex domain.
Finally, we show that the bulk-boundary correspondence in the Graf-Porta model of topological insulators is a special case of our result.