Eta invariants of the Berger spheres

08.02.2024, 16:00  –  Haus 9, Raum 0.14
Forschungsseminar Differentialgeometrie

Rebecca Roero

Presentation of an innovative way to compute the eta invariants for the Dirac operator of the Berger spheres. We can use the Atyiah-Patodi-Singer theorem for the index of the classical Dirac operator on a manifold with boundary, in order to write a formula that enables us to compute the eta invatiant of such operator on the boundary. This formula has an easy solution in particular for the eta invariants of the Berger spheres, that are in this case seen as boundary of the corresponding balls immersed in \CP^n. We can see the Berger metric as the one obtained restricting the Fubini Study metric to the sphere, and thus compute the integrals present in our formula. We will thus compute the eta invariant with our method and see that it matches its already known value.