Contents Introduction 1 Chapter 1. The Hubert manifold of i^-curves 3 Chapter 2. The loop space and the space of closed curves 15 Chapter 3. The second order neighborhood of a critical point 25 Appendix. The S1- and the Z2-action on AM 39 Chapter 4. Closed geodesics on spheres 45 Chapter 5. On the existence of infinitely many closed geodesics 59 References 77
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