Stacky Hamiltonian actions and symplectic reduction

Abstract

We introduce the notion of a Hamiltonian action of an étale Lie group stack on an étale symplectic stack and establish versions of the Kirwan convexity theorem, the Meyer-Marsden-Weinstein symplectic reduction theorem, and the Duistermaat-Heckman theorem in this context.

65 pages; appendix by Chenchang Zhu

References in corpus (8)

• Higher-Dimensional Algebra V: 2-Groups
• Foundations of Topological Stacks I
• Topological and Smooth Stacks
• Lie 2-algebras of vector fields
• Cohomological localization for transverse Lie algebra actions on Riemannian foliations
• The Derived Marsden-Weinstein Quotient is Symplectic
• Nonrational Symplectic Toric Reduction
• Left-invariant vector fields on a Lie 2-group

Cited by in corpus (5)

• Cohomological localization for transverse Lie algebra actions on Riemannian foliations
• The Basic de Rham Complex of a Singular Foliation
• Shifted coisotropic structures for differentiable stacks
• Toric Quasifolds
• The convexity package for Hamiltonian actions on conformal symplectic manifolds