2017/03/01 by Schaetz, Florian, Zambon, Marco · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1703.00290
We study the deformation theory of pre-symplectic structures, i.e. closed two-forms of fixed rank. The main result is a parametrization of nearby deformations of a given pre-symplectic structure in terms of an L_∞-algebra, which we call Koszul L_∞-algebra. This L_∞-algebra is a cousin of the Koszul dg Lie algebra associated to a Poisson manifold. In addition, we show that a quotient of the Koszul L∞-algebra is isomorphic to the L_∞-algebra which controls the deformations of the underlying characteristic foliation. Finally, we show that the infinitesimal deformations of pre-symplectic structures and of foliations are both obstructed.