{"id":"openai-math/Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples","pdf":"https://github.com/openai/math/blob/main/preprints/Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-October-7-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-October-7-2026","tags":["differential-geometry","symplectic-geometry","four-manifolds"],"score":0,"title":"Deforming hypersymplectic four-manifolds to hyperkähler triples","domain":"Differential geometry","family":"341","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"Every smooth normalized positive triple of closed two-forms on a closed connected oriented four-manifold admits a smooth deformation, with each cohomology class fixed, to a hyperkähler triple. This resolves Donaldson's hypersymplectic deformation conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-07","reactions":{},"formalized":false,"family_title":"Donaldson's hypersymplectic deformation conjecture"}