Shifted Contact Structures on Differentiable Stacks

Autor:	Maglio, Antonio, Tortorella, Alfonso G., Vitagliano, Luca
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry Mathematical Physics Mathematics - Symplectic Geometry 22A22 53D10 53D17 18N50
Druh dokumentu:	Working Paper
Popis:	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. Comment: 48 pages. Several improvements have been made. Final version to appear in Int. Math. Res. Not. IMRN
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.17661 Zobrazit plný text záznamu View this record from Arxiv