Algebra Seminar: Lesch -- The KO valued spectral flow for skewadjoint Fredholm operators

Matthias Lesch (University of Bonn) 

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

Title: The KO valued spectral flow for skewadjoint Fredholm operators

Abstract: 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.