On Tamed Almost Complex Four‑Manifolds  

作　　者：Qiang Tan Hongyu Wang Jiuru Zhou Peng Zhu 

机构地区：[1]School of Mathematical Sciences,Jiangsu University,Zhenjiang 212013,Jiangsu,China [2]School of Mathematical Sciences,Yangzhou University,Yangzhou 225002,Jiangsu,China [3]School of Mathematics and Physics,Jiangsu University of Technology,Changzhou 213001,Jiangsu,China

出　　处：《Peking Mathematical Journal》2022年第1期37-152,共116页北京数学杂志（英文）

基　　金：supported by PRC Grant NSFC 11701226(Tan),11371309,11771377(Wang),11426195(Zhou),11471145(Zhu);Natural Science Foundation of Jiangsu Province BK20170519(Tan);University Science Research Project of Jiangsu Province 15KJB110024(Zhou);Foundation of Yangzhou University 2015CXJ003(Zhou).

摘　　要：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.

关 键 词：ω-Tame(compatible)almost complex structure J-Anti-invariant cohomology Positive(1 1)current Local symplectic property J-Holomorphic curve 

分 类 号：O15[理学—数学]