Shifted symplectic higher Lie groupoids and classifying spaces

TL;DR

This paper introduces the concept of shifted symplectic structures on higher Lie groupoids, develops models for 2-shifted symplectic structures on classifying stacks, and constructs explicit symplectic Morita equivalences between these models.

Contribution

It defines m-shifted symplectic Lie n-groupoids and constructs explicit models and equivalences, advancing the understanding of symplectic structures in higher Lie groupoid theory.

Findings

Defined m-shifted symplectic Lie n-groupoids

Constructed models for 2-shifted symplectic structures

Established explicit symplectic Morita equivalences

Abstract

We introduce the concept of $m$-shifted symplectic Lie $n$-groupoids and symplectic Morita equivalences between them. We then build various models for the 2-shifted symplectic structure on the classifying stack in this setting and construct explicit symplectic Morita equivalences between them.