The cohomology ring of the boundary manifold of a combinatorial line arrangement
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909681422696448 |
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| author | Sugawara, Sakumi |
| author_facet | Sugawara, Sakumi |
| contents | Cohen--Suciu proved that the cohomology ring of the boundary manifold of a complex projective line arrangement is isomorphic to the double of the cohomology ring of the complement. In this paper, we generalize this result to arbitrary combinatorial line arrangements, including non-realizable ones. The notion of the boundary manifold for combinatorial line arrangements was introduced by Ruberman--Starkston. To handle arbitrary combinatorial line arrangements, we construct explicit homology cycles following the method by Doig--Horn. Using these cycles, we compute the cohomology ring of the boundary manifold and prove that it is isomorphic to the double of the Orlik-Solomon algebra. As an application, we derive several results on the resonance variety of the boundary manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06728 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The cohomology ring of the boundary manifold of a combinatorial line arrangement Sugawara, Sakumi Geometric Topology Combinatorics 32S22, 52C35, 05B35, 57K30 Cohen--Suciu proved that the cohomology ring of the boundary manifold of a complex projective line arrangement is isomorphic to the double of the cohomology ring of the complement. In this paper, we generalize this result to arbitrary combinatorial line arrangements, including non-realizable ones. The notion of the boundary manifold for combinatorial line arrangements was introduced by Ruberman--Starkston. To handle arbitrary combinatorial line arrangements, we construct explicit homology cycles following the method by Doig--Horn. Using these cycles, we compute the cohomology ring of the boundary manifold and prove that it is isomorphic to the double of the Orlik-Solomon algebra. As an application, we derive several results on the resonance variety of the boundary manifold. |
| title | The cohomology ring of the boundary manifold of a combinatorial line arrangement |
| topic | Geometric Topology Combinatorics 32S22, 52C35, 05B35, 57K30 |
| url | https://arxiv.org/abs/2507.06728 |