A Functional Analytic Index Theorem

26.11.2019, 16:15  –  Haus 9, Raum 1.10
Forschungsseminar Differentialgeometrie

Lennart Ronge (Bonn)

Considering a family of self-adjoint Fredholm operators A(t), the equality ind(D_APS)=sf(A) will be shown under certain conditions. Here, sf(A) denotes the spectral flow of the family A, D_APS is the closure of the operator d/dt-iA with certain (Atiyah-Patodi-Singer) boundary conditions and ind(D_APS) denotes its Fredholm index. Both sides of the equation are shown to be equal to the index of a Fredholm pair of projections that are related to the spectral projections of A and the evolution operator associated to A. This generalizes a result by C. Bär and A. Strohmaier used to show their Lorentzian version of the Atiyah-Patodi-Singer Index Theorem.