A Morse complex for Lorentzian geodesics

Details A Morse complex for Lorentzian geodesics A Morse complex for Lorentzian geodesics

2006-05-10

arxiv.org/abs/math/0605261v3

Asian Journal of Mathematics 12 (2008), 299-320

Mathematics

Differential Geometry

19 pages; updated references, final version

Scientific paper

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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