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 com...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.展开更多
基金supported by PRC Grant NSFC 11701226(Tan),11371309,11771377(Wang),11426195(Zhou),11471145(Zhu)Natural Science Foundation of Jiangsu Province BK20170519(Tan)+1 种基金University Science Research Project of Jiangsu Province 15KJB110024(Zhou)Foundation of Yangzhou University 2015CXJ003(Zhou).
文摘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.
