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

The orientation flow of paths of real skew-adjoint Fredholm operators with invertible endpoints was studied by Carey, Phillips and Schulz-Baldes. For paths of real skew-adjoint Fredholm operators with odd-dimensional kernel the 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 real skewadjoint Fredholm operators with odd-dimensional kernel to Z2. As an example the orientation flow of the magnetic flux inserted in a half-sided Kitaev chain is studied. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

The orientation flow of paths of real skew-adjoint Fredholm operators with invertible endpoints was studied, as well as the properties of paths with odd-dimensional kernel. The flow is independent of the reference projection when applied to closed paths, and provides an isomorphism to Z2 for the fundamental group of the space of real skewadjoint Fredholm operators with odd-dimensional kernel.