Event

Talk
An index theorem for compact Lorentzian manifolds with boundary
Prof. Dr. Christian Baer (U. Potsdam)
10 Nov 2015, 15:30 – 16:30

Starting with the classical Gauss-Bonnet theorem we give a short historical introduction to index theory. Then we show that the Dirac operator on a compact globally hyperbolic Lorentzian space-time with space like Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given formally by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary.

This is the first index theorem for Lorentzian manifolds and, from an analytic perspective, the methods to obtain it are quite different from the classical Riemannian case.