An equivariant index theorem on a Riemannian manifold.

17.10.2024, 16:15 Uhr  –  Raum 0.14
Forschungsseminar Differentialgeometrie

Onirban Islam

For differential operators preserved by the action of a Lie group G, the notion of index generalises to the G-index. A prototype of this situation arises for spin-Dirac operators on a compact Riemannian manifold which admits a non-trivial isometry group. This yields an equivariant index theorem known as the Atiyah-Segal-Singer index theorem. In this talk, I shall first introduce the notion of the G-index and then sketch a proof of the Atiyah-Segal-Singer index theorem by the heat kernel method due to Berline and Vergne.