On Tamed Almost Complex Four-Manifolds
Qiang Tan , Hongyu Wang , Jiuru Zhou , Peng Zhu
Peking Mathematical Journal ›› 2022, Vol. 5 ›› Issue (1) : 37 -152.
On Tamed Almost Complex Four-Manifolds
This paper proves that on any tamed closed almost complex four-manifold (M, J) whose dimension of J-anti-invariant cohomology is equal to the self-dual second Betti number minus one, there exists a new symplectic form compatible with the given almost complex structure J. In particular, if the self-dual second Betti number is one, we give an affirmative answer to a question of Donaldson for tamed closed almost complex four-manifolds. Our approach is along the lines used by Buchdahl to give a unified proof of the Kodaira conjecture.
National Natural Science Foundation of China(11701226)
Natural Science Foundation of Jiangsu Province(BK20170519)
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