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.

Ph.D. thesis, University of Florence, supervisors: Luca Vitagliano and Paolo de Bartolomeis, 174 pages