- AutorIn
- Michael Hecht
- Titel
- Isomorphic chain complexes of Hamiltonian dynamics on tori
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa-123279
- Datum der Einreichung
- 22.06.2012
- Datum der Verteidigung
- 17.07.2013
- Abstract (EN)
- 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.
- Freie Schlagwörter (DE)
- Floer Homologie, Morse Homologie, Kettenisomorphismus
- Freie Schlagwörter (EN)
- Floer homology, Morse homology, chain isomorphism
- Klassifikation (DDC)
- 500
- GutachterIn
- Prof. Dr. Matthias Schwarz
- Prof. Dr. Pietro Majer
- BetreuerIn
- Prof. Dr. Matthias Schwarz
- Den akademischen Grad verleihende / prüfende Institution
- Fakultät für Mathematik, Leipzig
- URN Qucosa
- urn:nbn:de:bsz:15-qucosa-123279
- Veröffentlichungsdatum Qucosa
- 02.10.2013
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch