Morse theory on the loop space of flat tori and symplectic Floer theory

Details Morse theory on the loop space of flat tori and symplectic Floer theory Morse theory on the loop space of flat tori and symplectic Floer theory

1996-12-16

arxiv.org/abs/dg-ga/9612012v2

Mathematics

Differential Geometry

14 pages, 1 figure

Scientific paper

We use closed geodesics to construct and compute Bott-type Morse homology groups for the energy functional on the loop space of flat $n$-dimensional tori, $n\ge 1$, and Bott-type Floer cohomology groups for their cotangent bundles equipped with the natural symplectic structure. Both objects are isomorpic to the singular homology of the loop space. In an appendix we perturb the equations in order to eliminate degeneracies and to get to a situation with nondegenerate critical points only. The (co)homology groups turn out to be invariant under the perturbation.

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