Asian Journal of Mathematics
Volume 12 (2008)
A Morse Complex for Lorentzian Geodesics
Pages: 299 – 320
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 every geodesic is infinite, and from the lack of the Palais-Smale condition, by using the Morse complex approach.
Geodesic; Lorentzian manifold; Morse complex
2010 Mathematics Subject Classification