A counterexample to the nearby Lagrangian conjecture
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.
Cite
@misc{OAI:A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026,
author = {{OpenAI}},
title = {{A counterexample to the nearby Lagrangian conjecture}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026/paper.pdf}{OAI:A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026}},
year = {2026}
}