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15 February 2022 Symplectic homology of convex domains and Clarke’s duality
Alberto Abbondandolo, Jungsoo Kang
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Duke Math. J. 171(3): 739-830 (15 February 2022). DOI: 10.1215/00127094-2021-0025

Abstract

We prove that the Floer complex associated with a convex Hamiltonian function on R2n is isomorphic to the Morse complex of Clarke’s dual action functional 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.

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Alberto Abbondandolo. Jungsoo Kang. "Symplectic homology of convex domains and Clarke’s duality." Duke Math. J. 171 (3) 739 - 830, 15 February 2022. https://doi.org/10.1215/00127094-2021-0025

Information

Received: 27 August 2019; Revised: 11 December 2020; Published: 15 February 2022
First available in Project Euclid: 17 February 2022

Digital Object Identifier: 10.1215/00127094-2021-0025

Subjects:
Primary: 53D40
Secondary: 52A20

Keywords: Clarke’s duality , convex domains , symplectic capacity , symplectic homology

Rights: Copyright © 2022 Duke University Press

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Vol.171 • No. 3 • 15 February 2022
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