论文标题
几乎复杂的4个manifolds的hodge-de rham数字
Hodge-de Rham numbers of almost complex 4-manifolds
论文作者
论文摘要
我们介绍并研究了紧凑的几乎复杂的4个manifolds的Hodge-de Rham数量，从而概括了复杂表面的Hodge数量。在复杂表面的情况下，这些数字的主要特性扩展到了更通用的环境，并且显示出所有用于紧凑型几乎复杂4个manifolds的Hodge-de rham数是由同胞确定的，除了一种（不规则性）。最后，这些数字被证明可以禁止在某些歧管上存在复杂结构，而无需参考表面的分类。
We introduce and study Hodge-de Rham numbers for compact almost complex 4-manifolds, generalizing the Hodge numbers of a complex surface. The main properties of these numbers in the case of complex surfaces are extended to this more general setting, and it is shown that all Hodge-de Rham numbers for compact almost complex 4-manifolds are determined by the cohomology, except for one (the irregularity). Finally, these numbers are shown to prohibit the existence of complex structures on certain manifolds, without reference to the classification of surfaces.
