Betti numbers and torsions in homology groups of double coverings
Betti numbers and torsions in homology groups of double coverings
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双覆盖同调群中的贝蒂数和挠率
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
M. Yoshinaga
中科院分区：
文献类型：
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作者：
Suguru Ishibashi;Sakumi Sugawara;M. Yoshinaga
Papadima和Suciu证明了有限域系数的Aomoto复形的上同调群和扭曲上同调群的秩之间的不等式，并证明了它们在与Milnor纤维相关的某些情况下实际上是相等的。最近，发现了一种具有以下两个特殊性质的排列（二十面体排列）：（i）严格的Papadima-Suciu不等式成立，（ii）Milnor纤维的第一积分同调具有非平凡的$2$-挠率。本文研究了双覆盖空间中这两个性质之间的关系。我们证明了（i）和（ii）实际上是等价的。
Papadima and Suciu proved an inequality between the ranks of the cohomology groups of the Aomoto complex with finite field coefficients and the twisted cohomology groups, and conjectured that they are actually equal for certain cases associated with the Milnor fiber of the arrangement. Recently, an arrangement (the icosidodecahedral arrangement) with the following two peculiar properties was found: (i) the strict version of Papadima-Suciu's inequality holds, and (ii) the first integral homology of the Milnor fiber has a non-trivial $2$-torsion. In this paper, we investigate the relationship between these two properties for double covering spaces. We prove that (i) and (ii) are actually equivalent.
双重覆盖和排列的积分局部系统上同调
DOI：
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发表时间：
2023
期刊：
影响因子：
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作者：
徳山 芳樹;串田 栞理;曵地 究;貴島 祐治;小出 陽平;Sakumi Sugawara
通讯作者：
Sakumi Sugawara