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Deforming hypersymplectic four-manifolds to hyperkähler triples

OpenAI · September 23, 2026

Earlier edition

This is an earlier edition (September 23, 2026). Current edition: Deforming hypersymplectic four-manifolds to hyperkähler triples, October 7, 2026.

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Cite

@misc{OAI:Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-September-23-2026,
  author = {{OpenAI}},
  title = {{Deforming hypersymplectic four-manifolds to hyperk\"ahler triples}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-September-23-2026/paper.pdf}{OAI:Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-September-23-2026}},
  year = {2026}
}

Family 341: Donaldson's hypersymplectic deformation conjecture

Proves Donaldson's hypersymplectic deformation conjecture in a cohomology-preserving form. Every positive triple of smooth closed two-forms on a closed connected oriented four-manifold, normalized by $\int\omega_i\wedge\omega_j=\delta_{ij}$, deforms through positive closed triples to a hyperkähler triple while preserving all three cohomology classes. Any positive triple can first be normalized by a constant linear change.

This is the only paper in this family.