Factorization of Dirac Operators on Riemannian Submersions

by Lucas Lemoine

Tuesday 14 May 2024, 16:00 → 18:00 Europe/Zurich

Sitzungszimmer (MI)

Take a Riemannian submersion between compact spin manifolds. J. Kaad and W. D. Van Suijlekom constructed two natural operators associated with this submersion. They first defined a family of Dirac operators on the fibers of the submersion, and then pulled back the Dirac operator of the base manifold to the total space. They showed that the tensor product of this two constructions is the Dirac operator on the total space, but only up to an explicit bounded curvature term! This result gives a more geometric outlook of the work of A. Connes, M. Hilsum, and G. Skandalis about wrong-way functoriality in a bounded setup, where this curvature term cannot be seen. After exposing their proof which takes place in (unbounded rather than bounded) KK-theory, I will reformulate their results in terms of groupoids, with the goal of eventually extending it to a certain class of foliations