Deformations of coisotropic submanifolds for fibrewise entire Poisson

Abstract

We show that deformations of a coisotropic submanifold inside a fibrewise entire Poisson manifold are controlled by the L∞-algebra introduced by Oh–Park (for symplectic manifolds) and Cattaneo–Felder. In the symplectic case, we recover results previously obtained by Oh–Park. Moreover we consider the extended deformation problem and prove its obstructedness.