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A Morse complex for Lorentzian geodesics

Alberto Abbondandolo·Pietro Majer
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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.

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Alberto Abbondandolo, Pietro Majer. 2008-09-25. A Morse complex for Lorentzian geodesics. https://arxiv.org/abs/math/0605261

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