A morse complex for Lorentzian geodesics

Abstract

We prove the Morse relations for the set of all geodesics connecting two non-conjugate points on a class of globally hyperbolic Lorentzian manifolds. We overcome the difficulties coming from the fact that the Morse index of geodesic is infinite, and from the lack of the Palais-Smale condition, by using the Morse complex approach. © 2008 International Press.