Reduction of symplectic groupoids and quotients of quasi-Poisson manifolds

TL;DR

This paper investigates the integrability of quotients of quasi-Poisson manifolds, unifying classical results and extending methods to double symplectic groupoids, advancing the understanding of Poisson and symplectic structures.

Contribution

It introduces a unified framework for Poisson quotient integrability and categorifies reduction methods to describe double symplectic groupoids.

Findings

Classical results on Poisson quotient integrability are unified.

A categorified reduction method for symplectic groupoids is developed.

Double symplectic groupoids for gauge groupoids are constructed.

Abstract

In this work we study the integrability of quotients of quasi-Poisson manifolds. Our approach allows us to put several classical results about the integrability of Poisson quotients in a common framework. By categorifying one of the already known methods of reducing symplectic groupoids we also describe double symplectic groupoids which integrate the recently introduced Poisson groupoid structures on gauge groupoids.