{"id":"openai-math/A-counterexample-to-the-nearby-Lagrangian-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026","tags":["symplectic-geometry","lagrangian-submanifolds","cotangent-bundles","floer-theory"],"score":0,"title":"A counterexample to the nearby Lagrangian conjecture","domain":"Differential geometry","family":"340","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"A counterexample to the nearby Lagrangian conjecture"}