双覆盖同调群中的贝蒂数和扭转

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-09-19 DOI:10.1016/j.aam.2024.102790

Suguru Ishibashi , Sakumi Sugawara , Masahiko Yoshinaga

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引用次数: 0

摘要

帕帕季马和苏修证明了具有有限场系数的青本复数同调群的秩与扭曲同调群之间的不等式，并猜想在与排列的米尔诺纤维相关的某些情况下，它们实际上是相等的。最近，我们发现了一种具有以下两个奇特性质的排列（icosidodecahedral arrangement）：(i) Papadima-Suciu 不等式的严格版本成立；(ii) Milnor 纤维的第一积分同调具有非三维 2 扭。在本文中，我们研究了双覆盖空间这两个性质之间的关系。我们证明(i)和(ii)实际上是等价的。

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Betti numbers and torsions in homology groups of double coverings

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.

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.