A Morse Complex for Lorentzian Geodesics

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.

Keywords

Geodesic, Lorentzian manifold, Morse complex

2010 Mathematics Subject Classification

53C50, 58E10

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Published 1 January 2008