Batalin-Vilkovisky algebra structure on the Hochschild cohomology of $E_\infty$-algebras
| Autor: | Razack, Ismaïl |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | When $\mathcal{M}$ is a smooth, oriented, compact and simply connected manifold, Luc Menichi has shown that $HH^\ast(C^\ast(\mathcal{M}; \mathbb{F}))$, the Hochschild cohomology of the singular cochain complex of $\mathcal{M}$ is a Batalin-Vilkovisky algebra. Using the properties of algebras over the Barratt-Eccles operad, we show that this results holds even when the manifold is not simply connected. Furthermore, we prove a similar result for pseudomanifolds. Namely, we explain why $HH^\ast_\bullet(\widetilde N^\ast_\bullet(X;\mathbb{F}))$, the Hochschild cohomology of the blown-up intersection cochain complex of a compact, oriented pseudomanifold $X$, is endowed with a Batalin-Vilkovisky algebra structure. Comment: 38 pages, comments are welcome. arXiv admin note: substantial text overlap with arXiv:2305.19054 |
| Databáze: | arXiv |
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