Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

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