Matroids, Feynman categories, and Koszul duality
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912150884188160 |
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| author | Coron, Basile |
| author_facet | Coron, Basile |
| contents | We show that various combinatorial invariants of matroids such as Chow rings and Orlik--Solomon algebras may be assembled into "operad-like" structures. Specifically, one obtains several operads over a certain Feynman category which we introduce and study in detail. In addition, we establish a Koszul-type duality between Chow rings and Orlik--Solomon algebras, vastly generalizing a celebrated result of Getzler. This provides a new interpretation of combinatorial Leray models of Orlik--Solomon algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_12370 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Matroids, Feynman categories, and Koszul duality Coron, Basile Combinatorics Algebraic Topology Category Theory We show that various combinatorial invariants of matroids such as Chow rings and Orlik--Solomon algebras may be assembled into "operad-like" structures. Specifically, one obtains several operads over a certain Feynman category which we introduce and study in detail. In addition, we establish a Koszul-type duality between Chow rings and Orlik--Solomon algebras, vastly generalizing a celebrated result of Getzler. This provides a new interpretation of combinatorial Leray models of Orlik--Solomon algebras. |
| title | Matroids, Feynman categories, and Koszul duality |
| topic | Combinatorics Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2211.12370 |