Poisson brackets and symplectic invariants

Abstract

We introduce new invariants associated to collections of compact subsets of a symplectic manifold. They are defined through an elementary-looking variational problem involving Poisson brackets. The proof of the non-triviality of these invariants involves various flavors of Floer theory. We present applications to approximation theory on symplectic manifolds and to Hamiltonian dynamics.

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References in corpus (3)

• C^0-rigidity of Poisson brackets
• Floer homology for negative line bundles and Reeb chords in pre-quantization spaces
• Floer cohomology and pencils of quadrics