Symplectic homology of convex domains and Clarke’s duality
Alberto Abbondandolo, Jungsoo Kang
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.
Topics & Concepts
MathematicsFloer homologySymplectic geometryPure mathematicsMorse homologySymplectomorphismSymplectic manifoldMoment mapCellular homologyAlgebra over a fieldGeometric and Algebraic TopologyHomotopy and Cohomology in Algebraic TopologyTopological and Geometric Data Analysis