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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… Click to show full 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.
Keywords:
symplectic homology;
convex domains;
convex;
domains clarke;
homology convex
Journal Title: Duke Mathematical Journal
Year Published: 2022
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Journal Title: Duke Mathematical Journal
Year Published: 2022
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!