Poisson sigma models and symplectic groupoids

@article{Cattaneo2000PoissonSM,
  title={Poisson sigma models and symplectic groupoids},
  author={A. Cattaneo and G. Felder},
  journal={arXiv: Symplectic Geometry},
  year={2000}
}
We consider the Poisson sigma model associated to a Poisson manifold. The perturbative quantization of this model yields the Kontsevich star product formula. We study here the classical model in the Hamiltonian formalism. The phase space is the space of leaves of a Hamiltonian foliation and has a natural groupoid structure. If it is a manifold then it is a symplectic groupoid for the given Poisson manifold. We study various families of examples. In particular, a global symplectic groupoid for a… Expand
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References

SHOWING 1-10 OF 20 REFERENCES
Deformation Quantization of Poisson Manifolds
POISSON STRUCTURE INDUCED (TOPOLOGICAL) FIELD THEORIES
ANALOGUES OF THE OBJECTS OF LIE GROUP THEORY FOR NONLINEAR POISSON BRACKETS
Two-Dimensional Gravity and Nonlinear Gauge Theory
Differential and Riemannian Manifolds
symplectiques et troisi ème th́eor̀eme de Lie non liń eaire, Lect
  • 1990
Karasev,Analogues of objects of Lie group theory for nonlinear Poiss n brackets, Math
  • USSR Izvestiya28
  • 1987
...
1
2
...