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- W12713440 abstract "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 using Morse theory, $SO(2)$- vs. $O(2)$-symmetries, Katok's examples and Finsler metrics, relations to symplectic geometry, and a guide to the literature. The Appendix written by Umberto Hryniewicz gives an account of the problem of the existence of infinitely many closed geodesics on the $2$-sphere." @default.
- W12713440 created "2016-06-24" @default.
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- W12713440 date "2014-06-11" @default.
- W12713440 modified "2023-09-26" @default.
- W12713440 title "Morse theory, closed geodesics, and the homology of free loop spaces" @default.
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