A survey on the Theorem of Chekhanov

Details A survey on the Theorem of Chekhanov A survey on the Theorem of Chekhanov

2009-12-02

arxiv.org/abs/0912.0439v1

Mathematics

Symplectic Geometry

This paper is a first work that precedes a paper on the coisotropic intersection problem

Scientific paper

The theorem of Chekhanov asserts that a Lagrangian submanifold L has positive displacement energy under natural assumptions on the symplectic topology at infinity. It is greater than or equal to the minimal area of holomorphic disks bounded by L. This estimate was obtained by Y.V. Chekhanov in 1998. Section 1 presents a direct proof based on the use of holomorphic curves and their Hamiltonian perturbations. In section 2, we define a filtered version of the Lagrangian Floer homology, without any assumption on L. This is compared with the Morse homology groups, via the continuation maps (subsubsection 2.3.2) or the PSS maps (subsection 3.2).

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