紧近复四维流形上的J-反变上同调及其应用  

On J-anti-invariant cohomology of compact almost complex fourmanifolds and applications

作　　者：王宏玉[1] 

机构地区：[1]扬州大学数学科学学院,扬州225002

出　　处：《中国科学：数学》2016年第5期697-708,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11371309)资助项目

摘　　要：本文作为综述,讨论了由Li和Zhang引入的闭近复流形上J-反变上同调的若干性质;特别地,利用与度量(辛形式)相容近复结构,探索了闭近Hermite(Khler)四维流形上的J-反变上同调子群H的维数h.本文还研究了闭辛流形上由Tseng和Yau引入的辛上同调群与J-反变上同调群的关系;对于自对偶第二Betti数为1的闭驯化四维近复流形,考虑了Donaldson问题.In this survey, we discuss some properties of J-anti-invariant cohomology introduced by Li and Zhang. In particular, we investigate properties of the dimension h of the J-anti-invariant cohomology subgroup H of closed almost Hermitian（Khler） four-manifolds using metric（symplectic form） compatible almost complex structures. We study the relationship between J-anti-invariant cohomology and new symplectic cohomologies introduced by Tseng and Yau on a closed symplectic manifold. Moreover, we consider Donaldson question for tamed closed almost complex four-manifolds with b~＋= 1.

关 键 词：J-反变上同调 辛上同调 ω-驯化(相容)近复结构 正(1 1)流 

分 类 号：O186.12[理学—数学]