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Abstract We give a Morse-theoretic characterization of simple closed geodesics on Riemannian 2-spheres. On any Riemannian 2-sphere endowed with a generic metric, we show there exists a simple closed geodesic with Morse index 1, 2 and 3. In particular, for an orientable Riemannian surface, we prove strong Morse inequalities for the length functional applied to the space of simple closed curves.
Dongyeong Ko (Tue,) studied this question.
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