2017/05/24 by Alfonso Giuseppe Tortorella, Tortorella, Alfonso Giuseppe
Mathematics · Medicine · #16E45 #53D10 #53D17 #53D35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1705.08962
openalex publication_date 2017/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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_∞[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_∞[1]-algebra and a BFV-complex to any coisotropic submanifold in a contact manifold. The L_∞[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.