Deformations of coisotropic submanifolds in abstract Jacobi manifolds

In this paper, using the Atiyah algebroid and first order multi-differential calculus on non-trivial line bundles, we attach an L_infinity-algebra to any coisotropic submanifold S in an abstract (or Kirillov's) Jacobi manifold. Our construction generalizes and unifies analogous constructions in symplectic, Poisson case, and locally conformal symplectic geometry. As a new special case, we attach an L_infinity-algebra to any coisotropic submanifold in a contact manifold, including Legendrian submanifolds. The L_infinity-algebra of a coisotropic submanifold S governs the (formal) deformation problem of S.