Multisymplectic Geometry and Lie Groupoids

@article{Bursztyn2015MultisymplecticGA,
  title={Multisymplectic Geometry and Lie Groupoids},
  author={H. Bursztyn and A. Cabrera and D. Iglesias},
  journal={arXiv: Symplectic Geometry},
  year={2015},
  pages={57-73}
}
We study higher-degree generalizations of symplectic groupoids, referred to as multisymplectic groupoids. Recalling that Poisson structures may be viewed as infinitesimal counterparts of symplectic groupoids, we describe “higher” versions of Poisson structures by identifying the infinitesimal counterparts of multisymplectic groupoids. Some basic examples and features are discussed. 
Quotients of multiplicative forms and Poisson reduction
Remarks on multisymplectic reduction
ON MULTISYMPLECTIC REDUCTION
On higher Dirac structures
Reduction of polysymplectic manifolds

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