Symplectic Forms and Cohomology Decomposition of almost Complex Four-Manifolds
Symplectic Forms and Cohomology Decomposition of almost Complex Four-Manifolds
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DOI：
10.1093/imrn/rnp113
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发表时间：
2008-12
影响因子：
1
通讯作者：
Tedi Drăghici;Tian-Jun Li;Weiyi Zhang
中科院分区：
文献类型：
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作者：
Tedi Drăghici;Tian-Jun Li;Weiyi Zhang
对于任意紧几乎复流形（M，J），后两位作者[8]定义了2次真实的de Rham上同调群的两个子群H + J（M），H − J（M）.这些是上同调类的集合，它们可以分别用J-不变的、J-反不变的真实的2-形式表示。在本文中，它表明，在4维这些子群诱导的上同调分解。这是一个具体的四维结果，因为它来自菲诺和托马西尼最近的工作[6]。当几乎复结构被辛形式所驯服时，这些群的维数也得到了一些估计，并给出了唐纳森问题的等价公式。
For any compact almost complex manifold (M, J), the last two authors [8] defined two subgroups H + J (M), H − J (M) of the degree 2 real de Rham cohomology group . These are the sets of cohomology classes which can be represented by J-invariant, respectively, J-antiinvariant real 2-forms. In this paper, it is shown that in dimension 4 these subgroups induce a cohomology decomposition of . This is a specifically four-dimensional result, as it follows from a recent work of Fino and Tomassini [6]. Some estimates for the dimensions of these groups are also established when the almost complex structure is tamed by a symplectic form and an equivalent formulation for a question of Donaldson is given.