Symplectic homology of convex domains and Clarke's duality
Abstract
We prove that the Floer complex that is associated with a convex Hamiltonian function on $\mathbb{R}^{2n}$ is isomorphic to the Morse complex of Clarke's dual action functional that is associated with the Fenchel-dual Hamiltonian. This isomorphism preserves the action filtrations. As a corollary, we obtain that the symplectic capacity from the symplectic homology of a convex domain with smooth boundary coincides with the minimal action of closed characteristics on its boundary.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2019
- DOI:
- 10.48550/arXiv.1907.07779
- arXiv:
- arXiv:1907.07779
- Bibcode:
- 2019arXiv190707779A
- Keywords:
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- Mathematics - Symplectic Geometry
- E-Print:
- 80 pages, v2: corrections in the proof of Lemma A.3, Appendix B added