A counterexample to the nearby Lagrangian conjecture
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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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For some sufficiently large even integer N, the manifold Q=S^9\times S^{N-1} admits a closed exact smoothly embedded Lagrangian L\subset T^*Q such that L is diffeomorphic to Q and no compactly supported Hamiltonian isotopy carries the zero section to L.
Reported proof verification
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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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Why this passage is shown
Theorem 1.1
In A counterexample to the nearby Lagrangian conjecture, 23 September 2026
How it was found
Its words were compared with the words of OpenAI’s catalogue description.