Batalin-Vilkovisky algebra structure on the Hochschild cohomology of $E_\infty$-algebras
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909156808589312 |
|---|---|
| author | Razack, Ismaïl |
| author_facet | Razack, Ismaïl |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Batalin-Vilkovisky algebra structure on the Hochschild cohomology of $E_\infty$-algebras Razack, Ismaïl Algebraic Topology 16E40, 55N33 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. |
| title | Batalin-Vilkovisky algebra structure on the Hochschild cohomology of $E_\infty$-algebras |
| topic | Algebraic Topology 16E40, 55N33 |
| url | https://arxiv.org/abs/2404.01323 |