In this thesis we construct for a given smooth, generic Hamiltonian
H on the 2n dimensional torus a chain-isomorphism between the Morse complex of the Hamiltonian action on the free loop space of the torus and the Floer-complex. Though both complexes are generated by the critical points of the Hamiltonian action, their boundary operators differ. Therefore the construction of the isomorphism is based on counting the moduli spaces of hybrid-type solutions which involves stating a new non-Lagrangian boundary value problem for Cauchy-Riemann type operators not yet studied in Floer theory.
It is crucial for the statement that the torus is compact, possesses trivial tangent bundle and an additive structure. We finally want to note that the problem is completely symmetric.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-123279 |
| Date | 02 October 2013 |
| Creators | Hecht, Michael |
| Contributors | Fakultät für Mathematik ,, Prof. Dr. Matthias Schwarz, Prof. Dr. Matthias Schwarz, Prof. Dr. Pietro Majer |
| Publisher | Universitätsbibliothek Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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