A hypergraph model for the cyclic BV operad and its applications
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912980755546112 |
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| author | Merkulov, Sergei |
| author_facet | Merkulov, Sergei |
| contents | A dg cyclic operad $BVHgraphs$ of hypergraphs is introduced which comes equipped with an explicit quasi-isomorphism $BV\rightarrow BVHgraphs$ from the { cyclic} operad $BV$ of Batalin-Vilkovisky algebras. A proof that the cohomology of $BVHgraphs$ equals $BV$ occupies most of this paper.
We use this model to construct an explicit quasi-isomorphism $Chains(FFM_2) \rightarrow BVHgraphs$ from the chain operad of the cyclic operad $FFM_2$ of the compactified moduli spaces of genus zero curves with marked framed points to the dg cyclic operad $BVHgraphs$ which, combined with the main result mentioned above, gives a new proof of the cyclic formality of $FFM_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23368 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A hypergraph model for the cyclic BV operad and its applications Merkulov, Sergei Algebraic Topology Quantum Algebra A dg cyclic operad $BVHgraphs$ of hypergraphs is introduced which comes equipped with an explicit quasi-isomorphism $BV\rightarrow BVHgraphs$ from the { cyclic} operad $BV$ of Batalin-Vilkovisky algebras. A proof that the cohomology of $BVHgraphs$ equals $BV$ occupies most of this paper. We use this model to construct an explicit quasi-isomorphism $Chains(FFM_2) \rightarrow BVHgraphs$ from the chain operad of the cyclic operad $FFM_2$ of the compactified moduli spaces of genus zero curves with marked framed points to the dg cyclic operad $BVHgraphs$ which, combined with the main result mentioned above, gives a new proof of the cyclic formality of $FFM_2$. |
| title | A hypergraph model for the cyclic BV operad and its applications |
| topic | Algebraic Topology Quantum Algebra |
| url | https://arxiv.org/abs/2603.23368 |