We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples include the shifted de Rham complex of a Poisson manifold and the subcomplex of differential forms on a symplectic manifold vanishing on a Lagrangian submanifold, endowed with the Koszul bracket. As a corollary we generalize a recent result by Hitchin on deformations of holomorphic Poisson manifolds.

FORMALITY OF KOSZUL BRACKETS AND DEFORMATIONS OF HOLOMORPHIC POISSON MANIFOLDS / Fiorenza, Domenico; Manetti, Marco. - In: HOMOLOGY, HOMOTOPY AND APPLICATIONS. - ISSN 1532-0073. - STAMPA. - 14:2(2012), pp. 63-75. [10.4310/hha.2012.v14.n2.a4]

FORMALITY OF KOSZUL BRACKETS AND DEFORMATIONS OF HOLOMORPHIC POISSON MANIFOLDS

FIORENZA, DOMENICO;MANETTI, Marco
2012

Abstract

We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples include the shifted de Rham complex of a Poisson manifold and the subcomplex of differential forms on a symplectic manifold vanishing on a Lagrangian submanifold, endowed with the Koszul bracket. As a corollary we generalize a recent result by Hitchin on deformations of holomorphic Poisson manifolds.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/486625
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