Symplectic groupoids of log symplectic manifolds
By M. Gualtieri, Songhao Li. 2012
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A log symplectic manifold is a Poisson manifold which is generically nondegenerate. We develop two methods for constructing the symplectic groupoids of log symplectic manifolds. The first is a blow-up construction, corresponding to the notion of an elementary modification of a Lie algebroid along a subalgebroid. The second is a gluing construction, whereby groupoids defined on the open sets of an appropriate cover may be combined to obtain global integrations. This allows us to classify all Hausdorff symplectic groupoids of log symplectic manifolds in a combinatorial fashion, in terms of a certain graph of fundamental groups associated to the manifold. Using the same ideas, and as a first step, we also construct and classify the groupoids integrating the Lie algebroid of vector fields tangent to a smooth hypersurface.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9e3d4620a613c8dcec879af407efa0bbec67453d
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In Mathematical Physics
Citations in the corpus
- Toric Actions on b-Symplectic Manifolds (2013, background): “the subject (in [GMP1] and [GMP2]) study the objects as manifolds with distinguished hypersurfaces. The symplectic groupoids integrating b-manifolds have been lately considered by Gualtieri and Li in [GL]. The topology of these manifolds have been studied further in [C], [FMM] and [MO1, MO2]. The cl”