Deformations of symplectic foliations. (English) Zbl 1494.53087
This paper develops the deformation theory of symplectic foliations. First, the authors describe the infinitesimal deformation of regular Poisson structures. Then, they deal with the constant rank condition. They establish that each symplectic foliation has an attached \(L_\infty\)-algebra controlling its deformation. They also show that its Maurer-Cartan elements correspond with the small deformations under the Dirac exponential map. Finally, the authors prove that the infinitesimal deformations of symplectic foliations can be obstructed. Links between symplectic foliations with Poisson structures are also described.
Reviewer: Angela Gammella-Mathieu (Metz)
MSC:
| 53D05 | Symplectic manifolds (general theory) |
| 53D17 | Poisson manifolds; Poisson groupoids and algebroids |
| 53C12 | Foliations (differential geometric aspects) |
| 58H15 | Deformations of general structures on manifolds |
Keywords:
deformations; symplectic foliations; \(L_\infty\) algebra; regular Poisson structures; Maurer Cartan elements; obstructions; Poisson geometry; Dirac geometryReferences:
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