Index Theory for Globally Hyperbolic Spacetimes

Abstract

An equality between the spectral flow of a family $A$ of self-adjoint Fredholm operators and the index of the associated differential operator $\frac{d}{dt}-iA$ with Atiyah-Patodi-Singer-style boundary conditions is shown. This generalizes a result by C.Bär and A. Strohmaier used to show their Lorentzian version of the Atiyah-Patodi-Singer Index Theorem.

This is the revised version of the author's master thesis, advised by Prof. Matthias Lesch and Dr. Koen van den Dungen at the University of Bonn

References in corpus (2)

• A noncommutative Atiyah-Patodi-Singer index theorem in KK-theory
• Families of spectral triples and foliations of space(time)

Cited by in corpus (2)

• Local Index Theory for Lorentzian Manifolds
• An index theorem on asymptotically static spacetimes with compact Cauchy surface