arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0812.3680math.SGmath.DG
收藏

殆复4-流形的辛形式与上同调分解

Symplectic forms and cohomology decomposition of almost complex 4-manifolds

Tedi Draghici, Tian-Jun Li, Weiyi Zhang

备注：
v2. This is the published version of some of the results of v1; Other parts of v1 have been considerably extended and included in arXiv:1104.2511
发表信息：
IMRN 2010, no. 1, 1-17
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

对于任何紧殆复流形$(M,J)$，最后两位作者在arXiv：0708.2520中定义了2次实de Rham上同调群$H^2(M, \mathbb{R})$的两个子群$H_J^+(M)$，$H_J^-(M)$。这些是可以分别用$J$ -不变、$J$ -反不变实$2-$形式表示的上同调类的集合。在这篇文章中，它表明，在4维这些子群诱导$H^2(M, \mathbb{R})$的上同调分解。这是一个具体的四维结果，因为它遵循菲诺和托马西尼最近的工作。当殆复结构被辛形式所驯服时，也建立了这些群的维数的一些估计，并给出了Donaldson问题的一个等价公式。

英文摘要：

For any compact almost complex manifold $(M,J)$, the last two authors defined two subgroups $H_J^+(M)$, $H_J^-(M)$ of the degree 2 real de Rham cohomology group $H^2(M, \mathbb{R})$ in arXiv:0708.2520. These are the sets of cohomology classes which can be represented by $J$-invariant, respectively, $J$-anti-invariant real $2-$forms. In this note, it is shown that in dimension 4 these subgroups induce a cohomology decomposition of $H^2(M, \mathbb{R})$. This is a specifically 4-dimensional result, as it follows from a recent work of Fino and Tomassini. 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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑