Preprint in the OpenAI Math release

A counterexample to the nearby Lagrangian conjecture

OpenAI

Abstract

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.

open until 1 Jan 2028

est. 50% chance this result is independently verified by the end of 2027.

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