Matroid complexes and Orlik-Solomon algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916797837475840 |
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| author | Coron, Basile |
| author_facet | Coron, Basile |
| contents | In this article we construct a combinatorial quasi-free differential graded model for the Orlik-Solomon algebra of supersolvable matroids, which generalizes in a matroidal setting the cdga of admissible graphs introduced by M. Kontsevich for the braid arrangements. Our construction draws on well-known concepts from matroid theory, including modularity, single-element extensions, and generalized parallel connections. We also show that this model carries a cooperadic structure in a suitably generalized sense. As an application, we use this model to give a new proof that the Orlik-Solomon algebras of supersolvable matroids are Koszul. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15048 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matroid complexes and Orlik-Solomon algebras Coron, Basile Combinatorics Algebraic Topology In this article we construct a combinatorial quasi-free differential graded model for the Orlik-Solomon algebra of supersolvable matroids, which generalizes in a matroidal setting the cdga of admissible graphs introduced by M. Kontsevich for the braid arrangements. Our construction draws on well-known concepts from matroid theory, including modularity, single-element extensions, and generalized parallel connections. We also show that this model carries a cooperadic structure in a suitably generalized sense. As an application, we use this model to give a new proof that the Orlik-Solomon algebras of supersolvable matroids are Koszul. |
| title | Matroid complexes and Orlik-Solomon algebras |
| topic | Combinatorics Algebraic Topology |
| url | https://arxiv.org/abs/2506.15048 |