CATALOGUE 340
A counterexample to the nearby Lagrangian conjecture
This single-manuscript catalogue belongs to the official subject Differential geometry. For some sufficiently large even $N$ and $Q=S^9\times S^{N-1}$, the manuscript claims a closed exact embedded Lagrangian diffeomorphic to the base but not Hamiltonian isotopic to the zero section. The article follows the nonzero tube class at infinity, the two-momentum embedding argument, and the contradiction obtained by transport to the zero section.
All manuscripts, in official catalogue order
These summaries give the principal scope; consult the cited original results for the complete hypotheses and statements.
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| # | Manuscript and overview | Principal claim | Role and available overview |
|---|---|---|---|
| 01 | A counterexample to the nearby Lagrangian conjecture →Short name: A counterexample to the nearby Lagrangian conjectureSeptember 23, 2026 · 28 pagesOriginal paper (GitHub) ↗ | For some sufficiently large even N, T*(S⁹×Sᴺ⁻¹) contains a closed exact embedded Lagrangian diffeomorphic to the base but not Hamiltonian isotopic to the zero section. Theorem 1.1 · p. 1 ↗ | Realize a nonzero stable tube class by a generating family, prove injectivity using two momenta, and apply one-critical-point vanishing after hypothetical transport. Read the proof overview → |
Sources and checking scope
OpenAI Research Catalog · Catalogue 340; Differential geometry · p. 37
The official list contains one manuscript, dated September 23, 2026, with 28 pages. The catalogue snapshot is 4eaee87548250b2682affda7d05d947c05554bae. Official catalogue number 340 is distinct from the article identifier.
The proof overview separates closedness, exactness, embedding, and diffeomorphism from the obstruction to Hamiltonian isotopy. The input table records the checked statements and applications from eleven directly used references, their versions, and the remaining verification limits. This is an overview based on reading the proof text in §§2–6, not complete independent proof verification. Remaining technical checks appear at the end of the article. Exhaustive dependencies on other catalogues remain uninvestigated.