University of Sydney Algebra Seminar

Matthias Lesch (University of Bonn)

Friday 3 May, 12-1pm, Place: Carslaw 375

The KO valued spectral flow for skewadjoint Fredholm operators

Roughly speaking the spectral flow of a path of selfadjoint Fredholm operators counts the net number of eigenvalues crossing 0. It is an interesting homotopy invariant, which e.g. is intimately related to the classifying spaces for the K-functor. According to Atiyah-Singers celebrated note on index theory for skew adjoint Fredholm operators the natural home for Fredholm indices is the space KO(point). In my talk I will review this story and develop a theory of a KO valued spectral flow. This is an ongoing project jointly with Bourne, Carey, and Rennie.