30.05.2025, 11:00
– Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis
TBA (Alfonso Garmendia)
Alfonso Garmendia (Bonn)
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.