Even torsions in the homology group of the Milnor fiber boundary of hyperplane arrangements in $\mathbb{C}^3$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908683821121536 |
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| author | Sugawara, Sakumi |
| author_facet | Sugawara, Sakumi |
| contents | We study the homology group of the Milnor fiber boundary of a hyperplane arrangement in $\mathbb{C}^{3}$. By the work of Némethi--Szilárd, the homeomorphism type of the Milnor fiber boundary is combinatorially determined, and an explicit formula for the first Betti number is known. However, the torsion part of the first homology group is poorly understood. In this paper, under some conditions, we prove that the number of even-order torsion summands of the first homology group is greater than or equal to the Euler characteristic of the projectivized complement. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_01371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Even torsions in the homology group of the Milnor fiber boundary of hyperplane arrangements in $\mathbb{C}^3$ Sugawara, Sakumi Algebraic Topology Combinatorics 52C35, 32S55 We study the homology group of the Milnor fiber boundary of a hyperplane arrangement in $\mathbb{C}^{3}$. By the work of Némethi--Szilárd, the homeomorphism type of the Milnor fiber boundary is combinatorially determined, and an explicit formula for the first Betti number is known. However, the torsion part of the first homology group is poorly understood. In this paper, under some conditions, we prove that the number of even-order torsion summands of the first homology group is greater than or equal to the Euler characteristic of the projectivized complement. |
| title | Even torsions in the homology group of the Milnor fiber boundary of hyperplane arrangements in $\mathbb{C}^3$ |
| topic | Algebraic Topology Combinatorics 52C35, 32S55 |
| url | https://arxiv.org/abs/2512.01371 |