Homology, Homotopy and Applications

Volume 14 (2012)

Number 2

Formality of Koszul brackets and deformations of holomorphic Poisson manifolds

Pages: 63 – 75

DOI: http://dx.doi.org/10.4310/HHA.2012.v14.n2.a4

Authors

Domenico Fiorenza (Università degli Studi di Roma “La Sapienza”, Dipartimento di Matematica “Guido Castelnuovo”, Roma, Italy)

Marco Manetti (Università degli Studi di Roma “La Sapienza”, Dipartimento di Matematica “Guido Castelnuovo”, Roma, Italy)

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.

Keywords

homotopical algebra, differential graded Lie algebra, Batalin-Vilkovisky algebra, deformation theory, Poisson manifold

2010 Mathematics Subject Classification

13D10, 18G55, 53D17

Full Text (PDF format)