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A counterexample to the nearby Lagrangian conjecture

Disproves the unrestricted nearby Lagrangian conjecture. For some sufficiently large even N, constructs a closed exact embedded Lagrangian in

T^*(S^9\times S^{N-1})

that is diffeomorphic to the base but not Hamiltonian isotopic to its zero section.

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A counterexample to the nearby Lagrangian conjecture

Sep 23, 2026·paper.pdf

We disprove the unrestricted nearby Lagrangian conjecture. For some sufficiently large even integer N, we construct a closed exact smoothly embedded Lagrangian in

T^*(S^9\times S^{N-1})

that is diffeomorphic to the base but is not Hamiltonian isotopic to the zero section.

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