|XXXIV Workshop on Geometric Methods in Physics||28.06-4.07.2015|
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Alfonso Giuseppe Tortorella
Deformations of coisotropic submanifolds in abstract Jacobi manifolds
ABSTRACT. In our work, using the Atiyah algebroid and first order multi-differential calculus on non-trivial line bundles, we attach an $L_\infty$-algebra to any coisotropic submanifold $S$ in an abstract (or Kirillov's) Jacobi manifold. Our construction generalizes and unifies analogous constructions in  (symplectic case),  (Poisson case),  (locally conformal symplectic case). As a new special case, we attach an $L_\infty$-algebra to any coisotropic submanifold in a contact manifold, including Legendrian submanifolds. The $L_\infty$-algebra of a coisotropic submanifold $S$ governs the (formal) deformation problem of $S$.
 A.S. Cattaneo and G. Felder, Relative formality theorem and quantisation of coisotropic submanifolds, Adv. Math. 208 (2007) 521-548.
 H.V. Lê and Y.-G. Oh, Deformations of coisotropic submanifolds in locally conformal symplectic manifolds, arXiv:1208.3590}, to appear in Asian J. Math.
 H.V. Lê, Y.-G. Oh, A.G. Tortorella, and L. Vitagliano, Deformations of coisotropic submanifolds in abstract Jacobi manifolds, arXiv:1410.8446.
 Y.-G. Oh and J.-S. Park, Deformations of coisotropic submanifolds and strong homotopy Lie algebroids, Invent. Math. 161 (2005) 287--360.