08.05.2025, 16:15
– Haus 9, Raum 1.22
Forschungsseminar Differentialgeometrie
Scalar Curvature Rigidity and Higher Index Theory
Thomas Tony
Remo Ziemke
This thesis generalizes Getzler's spectral flow formula for twisted Dirac operators to arbitrary twisting bundles and 1-parameter-families of connections. The formula proved by Getzler states that
\[\mathsf{sf}\big(D^{d + sh^{-1}(dh)}\big) = -\frac{1}{(-2\pi i)^{k+1}}\int_M \hat{\mathsf{A}}(TM) \wedge \mathsf{ch}(h)\]
where \(h\colon M^{2k+1} \to U(N)\) is a unitary matrix valued map on a closed Riemannian spin manifold and \(\mathsf{ch}(h)\) is the odd Chern character.