• Corpus ID: 115934673

Morse theory, closed geodesics, and the homology of free loop spaces

@article{Oancea2014MorseTC,
  title={Morse theory, closed geodesics, and the homology of free loop spaces},
  author={Alexandru Oancea},
  journal={arXiv: Differential Geometry},
  year={2014}
}
  • A. Oancea
  • Published 11 June 2014
  • Mathematics
  • arXiv: Differential Geometry
This is a survey paper on Morse theory and the existence problem for closed geodesics. The free loop space plays a central role, since closed geodesics are critical points of the energy functional. As such, they can be analyzed through variational methods. The topics that we discuss include: Riemannian background, the Lyusternik-Fet theorem, the Lyusternik-Schnirelmann principle of subordinated classes, the Gromoll-Meyer theorem, Bott's iteration of the index formulas, homological computations… 

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