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.
Deformations of coisotropic submanifolds in abstract Jacobi manifolds
TORTORELLA, ALFONSO GIUSEPPE;
In corso di stampa
Abstract
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.File in questo prodotto:
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