Lagrangian Poincaré Recurrence via pseudoholomorphic foliations

Abstract: For any Hamiltonian displaceable closed curve inside a closed symplectic surface, there is a bound on the number of pairwise disjoint Hamiltonian isotopic copies of the curve that one can produce. This phenomenon is called Lagrangian Poincaré Recurrence, and it was only shown very recently by Polterovich and Shelukhin that there exist displaceable Lagrangians in higher dimension that satisfy the analogous property. In this work in progress joint with E. Opshtein, we use the technique of pseudoholomorphic foliations to show that the bound on the number of disjoint copies in the surface persists after increasing the dimension by the following stabilisation: take the cartesian product of the symplectic surface with a sufficiently small symplectic annulus, and take the product of the curve with the with the core of the annulus to produce a Lagrangian torus.

mathematical physicsalgebraic geometrysymplectic geometry

Audience: researchers in the topic

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