Perturbations of APS Boundary Conditions for Lorentzian Dirac Operators

Lennart  Ronge

Universität Potsdam, Haus 9, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany

Abstract: We study how far APS boundary conditions for a Lorentzian Dirac operator may be perturbed without destroying Fredholmness of the Dirac operator. This is done by developing criteria under which the perturbation of a compact pair of projections is a Fredholm pair.

Keywords: index theory, Fredholm pairs, Lorentzian geometry, boundary value problems.

MSC: 58J20, 58J45, 58J32, 47A53

Received: May 20, 2025; in final form October 9, 2025; Published online October 20, 2025

Language: English

DOI: 10.3842/SIGMA.2025.088

ArXiv: 2408.16696