Relative formality theorem and quantisation of coisotropic submanifolds. (English) Zbl 1106.53060

Cattaneo, Alberto S.; Felder, Giovanni

Adv. Math. 208, No. 2, 521-548 (2007).

This paper proves a version of Kontsevich’s formality theorem for supermanifolds. In 1997, M. Kontsevich showed his formality theorem which gives a solution to the deformation quantization problem. In this work, the authors show a relative version of this theorem. They show that the differential graded Lie algebra of multidifferential operators is quasi-isomorphic to its cohomology. Applications for coisotropic submanifolds are then given. The interpretation of the results in term of topological quantum field theory is also discussed. In particular, the duality between the Poisson sigma model on a manifold and the Poisson sigma model on a associated supermanifold is etablished.

Reviewer: Angela Gammella (Creil)

MSC:

53D55	Deformation quantization, star products
53D17	Poisson manifolds; Poisson groupoids and algebroids

Keywords:

formality theorem; deformation quantization; coisotropic manifolds; supermanifold

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