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.
released 2026-10-07 | 7 theorems · 33 lemmas · 54 proofs · 38,447 words |
PLAY LEVEL 1 »(pdf)
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.