Hamiltonian group actions on symplectic Deligne-Mumford stacks and toric orbifolds

TL;DR

This paper extends Hamiltonian group actions and symplectic reduction to the setting of symplectic Deligne-Mumford stacks, introducing new examples of symplectic toric orbifolds via quotients involving non-abelian groups.

Contribution

It develops the differential and symplectic geometry of Deligne-Mumford stacks and constructs new symplectic toric stacks as quotients involving non-abelian groups.

Findings

New framework for Hamiltonian actions on stacks

Construction of symplectic toric DM stacks as quotients

Examples involving non-abelian finite groups

Abstract

We develop differential and symplectic geometry of differentiable Deligne-Mumford stacks (orbifolds) including Hamiltonian group actions and symplectic reduction. As an application we construct new examples of symplectic toric DM stacks as symplectic quotients of C^NxBG, where G is a finite non-abelian group.