Nearby Lagrangian conjecture
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In mathematics, more specifically symplectic topology, the nearby Lagrangian conjecture, is an open[1] mathematical problem often attributed to Vladimir Arnold. It states that every closed exact Lagrangian submanifold of a cotangent bundle T∗M (with symplectic structure) is Hamiltonian isotopic to the zero section.[2][3][4]
Unsolved problem in mathematics
Prove or disprove: Any closed exact Lagrangian submanifold of the cotangent bundle of a closed manifold is Hamiltonian isotopic to the zero section.
It is closely related to the theory of generating functions.[5]
