Deformations of coisotropic submanifolds in Jacobi manifolds

Abstract: In this thesis, we study the deformation problem of coisotropic submanifolds in Jacobi manifolds. In particular we attach two algebraic invariants to any coisotropic submanifold $S$ in a Jacobi manifold, namely the $L_\infty[1]$-algebra and the BFV-complex of $S$. Our construction generalizes and unifies analogous constructions in symplectic, Poisson, and locally conformal symplectic geometry. As a new special case we also attach an $L_\infty[1]$-algebra and a BFV-complex to any coisotropic submanifold in a contact manifold. The $L_\infty[1]$-algebra of $S$ controls the formal coisotropic deformation problem of $S$, even under Hamiltonian equivalence. The BFV-complex of $S$ controls the non-formal coisotropic deformation problem of $S$, even under both Hamiltonian and Jacobi equivalence. In view of these results, we exhibit, in the contact setting, two examples of coisotropic submanifolds whose coisotropic deformation problem is obstructed.