Formality of Koszul brackets and deformations of holomorphic Poisson manifolds

Details Formality of Koszul brackets and deformations of holomorphic Poisson manifolds Formality of Koszul brackets and deformations of holomorphic Poisson manifolds

2011-09-20

arxiv.org/abs/1109.4309v2

Mathematics

Quantum Algebra

9 pages; exposition improved; new examples included; references added. We learned from Florian Schaetz that Theorem 1.2 is ori

Scientific paper

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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