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Cup-length estimate for Lagrangian intersections

Chun-gen Liu
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Abstract

In this paper we consider the Arnold conjecture on the Lagrangian intersections of some closed Lagrangian submanifold of a closed symplectic manifold with its image of a Hamiltonian diffeomorphism. We prove that if the Hofer's symplectic energy of the Hamiltonian diffeomorphism is less than a topology number defined by the Lagrangian submanifold, then the Arnold conjecture is true in the degenerated (non-transversal) case.

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Chun-gen Liu. 2003-04-07. Cup-length estimate for Lagrangian intersections. https://arxiv.org/abs/math/0304097

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