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Moduli of coisotropic sections and the BFV-complex. (English) Zbl 1237.53078

This paper deals with the local deformation of coisotropic submanifolds inside Poisson manifolds. Let us recall that the coisotropic submanifolds of symplectic manifolds are natural submanifolds containing Lagrangians submanifolds and that the notion of coisotropic submanifolds can be directly generalized to Poisson structures. In this work, the author introduces the appropriate equivalence relation on the set of coisotropic submanifolds. Then, he recalls the basic facts about the construction of the BFV-complex. He considers a groupoid structure on the set of the geometric Maurer-Cartan elements of this complex. The author introduces a surjective morphism from the groupoid of the BFV-complex to the groupoid of coisotropic sections, and characterizes the kernel of this morphism. Finally, an isomorphism between the moduli of coisotropic sections and the groupoid of the BFV-complex is obtained. This work gives a new approach to the problem of the local deformation of coisotropic submanifolds. Moreover, it enables a better understanding of the geometry of the BFV-complex.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
16E45 Differential graded algebras and applications (associative algebraic aspects)