On the J-anti-invariant cohomology of almost complex 4-manifolds
On the J-anti-invariant cohomology of almost complex 4-manifolds
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DOI：
10.1093/qmath/har034
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发表时间：
2011-04
影响因子：
0.7
通讯作者：
Tedi Drăghici;Tian-Jun Li;Weiyi Zhang
中科院分区：
文献类型：
--
作者：
Tedi Drăghici;Tian-Jun Li;Weiyi Zhang
对于紧致几乎复4-流形$（M，J）$，我们研究了$H^2（M，\mathbb{R}）$的子群$H^{\pm}_J$，这些子群分别由$J$-不变量和$J$-反不变量2-形式表示的上同调类组成.若$B^+ =1$，我们证明了对于$M$上的一般几乎复结构，子群$H^-_J$是平凡的.对于与可积结构相关的几乎复结构，给出了子群及其维数h^{\pm}_J$的计算.我们还证明了$h^{\pm}_J$的半连续性。
For a compact almost complex 4-manifold $(M,J)$, we study the subgroups $H^{\pm}_J$ of $H^2(M, \mathbb{R})$ consisting of cohomology classes representable by $J$-invariant, respectively, $J$-anti-invariant 2-forms. If $b^+ =1$, we show that for generic almost complex structures on $M$, the subgroup $H^-_J$ is trivial. Computations of the subgroups and their dimensions $h^{\pm}_J$ are obtained for almost complex structures related to integrable ones. We also prove semi-continuity properties for $h^{\pm}_J$.