Homology, Homotopy and Applications
Volume 14 (2012)
Formality of Koszul brackets and deformations of holomorphic Poisson manifolds
Pages: 63 – 75
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.
homotopical algebra, differential graded Lie algebra, Batalin-Vilkovisky algebra, deformation theory, Poisson manifold
2010 Mathematics Subject Classification
13D10, 18G55, 53D17