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

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.