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 every geodesic is infinite, and from the lack of the Palais-Smale condition, by using the Morse complex approach.

19 pages; updated references, final version

References in corpus (1)

• A Morse complex for infinite dimensional manifolds - Part I

Cited by in corpus (2)

• On a formula for the spectral flow and its applications
• Genericity of nondegenerate critical points and Morse geodesic functionals