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arXiv · 2306.17661

Shifted Contact Structures on Differentiable Stacks

Antonio Maglio·Alfonso G. Tortorella·Luca Vitagliano
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Abstract

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.

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BibTeXRIS

Antonio Maglio, Alfonso G. Tortorella, Luca Vitagliano. 2023-06-30. Shifted Contact Structures on Differentiable Stacks. https://arxiv.org/abs/2306.17661

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