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 mathématiquesIntervenant-e-s
Benjamin Hoffman, Cornellentrée libre
Classement
Catégorie: Séminaire