Spectral flow of twisted Dirac operators

12.05.2025, 14:00  –  Haus 9, Raum 2.22
Verteidigung Masterarbeit / Master's Thesis Defence

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.