OpenAI research collection · 1 manuscript · Source checked 2026-10-19
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.
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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.
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