# Stacky Hamiltonian actions and their moment polytopes (Benjamin Hoffman, Cornell)

17.04.2018 15:30

Given a Hamiltonian action of a Lie group $G$ on a symplectic manifold $(M, \omega)$, you can understand $M$ via its image under the moment map $\mu: M\to \mathfrak{g}^*$, which is sometimes a rational convex polytope.

A natural question is to what spaces can be associated non-rational moment polytopes. We answer this by describing Hamiltonian stacks, which are built by taking the stacky quotient of a presymplectic manifold by its null foliation. Hamiltonian stacks come with an action of a Lie group stack $\mathcal{G}$, and a moment map taking values in the dual of the Lie algebra of $\mathcal{G}$.

After developing the basic theory we construct the symplectic reduction of a Hamiltonian stack and extend the Duistermaat-Heckman theorem.

This work is joint with Reyer Sjamaar.

### Lieu

Bâtiment: Battelle

Séminaire "Groupes de Lie et espaces des modules"

### Organisé par

Section de mathématiques

### Intervenants

Benjamin Hoffman, Cornell

entrée libre

### Classement

Catégorie: Séminaire