Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

In this talk, following works by Schaetz, I will review the construction of the BV-complex and its role in the coisotropic deformation problem. In a Poisson manifold, each coisotropic submanifold comes attached with two cohomological resolutions of its reduced Poisson algebra. The first one is the L-infinity-algebra introduced by Oh&Park in the symplectic case, and by Cattaneo&Felder in the Poisson case. As well-known this L-infinity-algebra controls the formal coisotropic deformation problem, and under a generically non-trivial necessary and sufficient condition the non-formal deformation as well. The second one is the BV-complex originally introduced by physicists dealing with Hamiltonian systems with symmetries. As proved by Schaetz, the BV-complex and the L-infinity-algebra are L-infinity quasi-isomorphic, and so they control equally well the formal coisotropic deformation problem. However, as proven by Schaetz, the BV-complex encodes also further information about the non-formal deformations, which generically is not captured by the L-infinity-algebra. If time permits I will start to describe how these results can be transferred into the more general framework of Jacobi manifolds.