Shifted Contact Structures on Differentiable Stacks

Author:

Antonio Maglio, Alfonso G. Tortorella, Luca Vitagliano

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Mathematical Physics (math-ph), Symplectic Geometry (math.SG)

journal:

date:

2023-06-29 16:00:00

Abstract

We define $0$-shifted and $+1$-shifted contact structures on differentiable stacks, thus laying the foundations of 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 vector bundle in the category of Lie groupoids but it) always exists as a vector bundle in the category of differentiable stacks, 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.

PDF: Shifted Contact Structures on Differentiable Stacks.pdf