Shifted Contact Structures on Differentiable Stacks

TL;DR

This paper introduces the concept of shifted contact structures on differentiable stacks, establishing a new framework in shifted contact geometry and relating it to shifted symplectic structures, with applications to orbifolds and prequantum bundles.

Contribution

It defines 0- and +1-shifted contact structures on differentiable stacks, creating the foundation for shifted contact geometry and connecting it to shifted symplectic structures.

Findings

Kernel of a multiplicative 1-form exists as a differentiable stack

Examples of 0-shifted contact structures include contact structures on orbifolds

Examples of +1-shifted contact structures include prequantum bundles over shifted symplectic groupoids

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.