Article Dans Une Revue Compositio Mathematica Année : 2015

Simultaneous deformations and Poisson geometry

Résumé

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an L-infinity algebra, which we construct explicitly. Our machinery is based on Th. Voronov's derived bracket construction. In this paper we consider only geometric applications, including deformations of coisotropic submanifolds in Poisson manifolds, of twisted Poisson structures, and of complex structures within generalized complex geometry. These applications can not be, to our knowledge, obtained by other methods such as operad theory.

Dates et versions

hal-03174967 , version 1 (19-03-2021)

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Citer

Yaël Frégier, Marco Zambon. Simultaneous deformations and Poisson geometry. Compositio Mathematica, 2015, 151 (9), pp.1763-1790. ⟨10.1112/S0010437X15007277⟩. ⟨hal-03174967⟩

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