Orientation flow for real skew-adjoint Fredholm operators with odd-dimensional kernel

The orientation flow of paths of bounded real skew-adjoint Fredholm operators with invertible endpoints was studied by Carey, Phillips and Schulz-Baldes. In this talk, an orientation flow of norm-continuous paths of bounded real skew-adjoint Fredholm operators with odd-dimensional kernel is introduced and studied. This orientation flow is defined with respect to a real one-dimensional reference projection. It is homotopy invariant and fulfills a concatenation property. When applied to closed paths it is independent of the reference projection and provides an isomorphism of the fundamental group of the space of bounded real skew-adjoint Fredholm operators with odd-dimensional kernel, equipped with the norm topology, to Z2.