{"id":"openai-math/Taming-implies-compatibility-on-four-manifolds","pdf":"https://github.com/openai/math/blob/main/preprints/Taming-implies-compatibility-on-four-manifolds-October-6-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Taming-implies-compatibility-on-four-manifolds-October-6-2026","tags":["symplectic-geometry","almost-complex-structures","four-manifolds"],"score":0,"title":"Taming implies compatibility on four-manifolds","domain":"Differential geometry","family":"342","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We prove that every smooth almost complex structure on a closed four-manifold which is tamed by a symplectic form is compatible with a symplectic form. This gives a positive solution to Donaldson's tamed-to-compatible conjecture. We also characterize the compatible cone by strict intersection positivity on the closure of the invariant part of the taming cone.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-06","reactions":{},"formalized":false,"family_title":"Donaldson's tamed-to-compatible conjecture"}