Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 237

Relation between Morse theory of closed geodesics of $S^{1}$and symplectic Floer theory of $T^{*}S^{1}$

J. Weber

We construct Bott-type Floer homology groups for the symplectic manifold $(T^{*}S^{1},Omega_{can} )$ and Bott-type Morse homology groups for the energy functional on the loop space of $S^{1}$. Both objects turn out to be isomorpic to the singular homology of the loop space of $S^{1}$. So far our objects depend on all choices involved, but the above isomorphism suggests further investigation to show independence of these choices as well as a generalization to any closed riemannian manifold.

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