Formal geometry and Tamarkin--Tsygan calculi of dg manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912712293875712 |
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| author | Liao, Hsuan-Yi Stiénon, Mathieu Xu, Ping |
| author_facet | Liao, Hsuan-Yi Stiénon, Mathieu Xu, Ping |
| contents | The main goal of this paper is to study the formal geometry of dg manifolds à la Fedosov. For any dg manifold $(\mathcal{M}, Q)$, we construct a Fedosov dg foliation (or dg Lie algebroid) $\mathcal{F}_Q \to \mathcal{N}_Q$. We establish homotopy contractions between their respective spaces of polyvector fields, differential forms, polydifferential operators, and polyjets. As a consequence, we prove that their respective Cartan calculi and noncommutative calculi, in the sense of Tamarkin--Tsygan, are isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12399 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formal geometry and Tamarkin--Tsygan calculi of dg manifolds Liao, Hsuan-Yi Stiénon, Mathieu Xu, Ping Differential Geometry High Energy Physics - Theory Quantum Algebra The main goal of this paper is to study the formal geometry of dg manifolds à la Fedosov. For any dg manifold $(\mathcal{M}, Q)$, we construct a Fedosov dg foliation (or dg Lie algebroid) $\mathcal{F}_Q \to \mathcal{N}_Q$. We establish homotopy contractions between their respective spaces of polyvector fields, differential forms, polydifferential operators, and polyjets. As a consequence, we prove that their respective Cartan calculi and noncommutative calculi, in the sense of Tamarkin--Tsygan, are isomorphic. |
| title | Formal geometry and Tamarkin--Tsygan calculi of dg manifolds |
| topic | Differential Geometry High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2511.12399 |