Asian Journal of Mathematics

Volume 12 (2008)

Number 3

A Morse Complex for Lorentzian Geodesics

Pages: 299 – 320



Alberto Abbondandolo

Pietro Majer


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

53C50, 58E10

Published 1 January 2008