Shifted Contact Structures on Differentiable Stacks
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909233411260416 |
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| author | Maglio, Antonio Tortorella, Alfonso G. Vitagliano, Luca |
| author_facet | Maglio, Antonio Tortorella, Alfonso G. Vitagliano, Luca |
| contents | We define \emph{$0$-shifted} and \emph{$+1$-shifted contact structures} on differentiable stacks, thus laying the foundations of \emph{shifted Contact Geometry}. As a side result we show that the kernel of a multiplicative $1$-form on a Lie groupoid (might not exist as a Lie groupoid but it) always exists as a differentiable stack, and it is naturally equipped with a stacky version of the curvature of a distribution. Contact structures on orbifolds provide examples of $0$-shifted contact structures, while prequantum bundles over $+1$-shifted symplectic groupoids provide examples of $+1$-shifted contact structures. Our shifted contact structures are related to shifted symplectic structures via a Symplectic-to-Contact Dictionary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_17661 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Shifted Contact Structures on Differentiable Stacks Maglio, Antonio Tortorella, Alfonso G. Vitagliano, Luca Differential Geometry Mathematical Physics Symplectic Geometry 22A22, 53D10, 53D17, 18N50 We define \emph{$0$-shifted} and \emph{$+1$-shifted contact structures} on differentiable stacks, thus laying the foundations of \emph{shifted Contact Geometry}. As a side result we show that the kernel of a multiplicative $1$-form on a Lie groupoid (might not exist as a Lie groupoid but it) always exists as a differentiable stack, and it is naturally equipped with a stacky version of the curvature of a distribution. Contact structures on orbifolds provide examples of $0$-shifted contact structures, while prequantum bundles over $+1$-shifted symplectic groupoids provide examples of $+1$-shifted contact structures. Our shifted contact structures are related to shifted symplectic structures via a Symplectic-to-Contact Dictionary. |
| title | Shifted Contact Structures on Differentiable Stacks |
| topic | Differential Geometry Mathematical Physics Symplectic Geometry 22A22, 53D10, 53D17, 18N50 |
| url | https://arxiv.org/abs/2306.17661 |