Asian Journal of Mathematics

A Morse Complex for Lorentzian Geodesics

Alberto Abbondandolo and 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.

Article information

Source
Asian J. Math., Volume 12, Number 3 (2008), 299-320.

Dates
First available in Project Euclid: 12 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1226527085

Mathematical Reviews number (MathSciNet)
MR2453558

Zentralblatt MATH identifier
1166.58009

Subjects
Primary: 58E10: Applications to the theory of geodesics (problems in one independent variable) 53C50: Lorentz manifolds, manifolds with indefinite metrics

Keywords
Geodesic Lorentzian manifold Morse complex

Citation

Abbondandolo, Alberto; Majer, Pietro. A Morse Complex for Lorentzian Geodesics. Asian J. Math. 12 (2008), no. 3, 299--320. https://projecteuclid.org/euclid.ajm/1226527085


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