In \cite{btoric}, Guillemin et al. proved a Delzant-type theorem which classifies -symplectic toric manifolds. More generally, in \cite{torus} they proved a similar convexity result for general Hamiltonian torus action on -symplectic manifolds. In this paper, we provide a new way to construct -symplectic toric…
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10 results for “b-symplectic”
Quantizes -symplectic toric manifolds using -modules.
problem Quantization of -symplectic toric manifolds.
method Bohr-Sommerfeld quantization via -modules.
result Dimension of quantization coincides with signed count of integral points in moment polytope.
We study a notion of pre-quantization for -symplectic manifolds. We use it to construct a formal geometric quantization of -symplectic manifolds equipped with Hamiltonian torus actions with nonzero modular weight. We show that these quantizations are finite dimensional -modules.
In [GMPS] we proved that the moment map image of a -symplectic toric manifold is a convex -polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on -symplectic manifolds. The modular weights of the action on the connected components of the exceptio…
We compute the Picard group of a stable b-symplectic manifold by introducing a collection of discrete invariants which classify up to Morita equivalence.
Introduces -Lie groups and studies their symplectic structures and reductions.
problem Developing a theoretical framework for space-time transformations.
method Introduces -Lie groups and studies their canonical -symplectic structures and reductions.
result Poisson reduction under cotangent lifted action of can be described using Lie algebra structures.
Reduces symplectic manifolds with singularities for quantum reduction.
problem Quantization commutes with reduction for singular symplectic manifolds.
method Reduction theory for -symplectic manifolds and folded symplectic manifolds under general symmetries.
result New constructions of (singular) quasi-Hamiltonian spaces via reduction and fusion product.
New action-angle coordinates found for singular symplectic manifolds.
problem Existence of action-angle coordinates for singular symplectic manifolds.
method Action-angle theorem for folded symplectic integrable systems.
result New topological obstructions found for global existence of action-angle coordinates.
Stacks in Poisson Geometrymath.DG
This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between the bicategory of internal groupoids and the bicategory of geometric stacks. The s…
Tichler proved that a manifold admitting a smooth closed one-form fibers over a circle. More generally a manifold admitting independent closed one-forms fibers over a torus . In this article we explain a version of this construction for manifolds with boundary using the techniques of -calculus. We explore n…