Alfonso Giuseppe Tortorella

Deformations of coisotropic submanifolds in abstract Jacobi manifolds

ABSTRACT. In our work[3], 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 [4] (symplectic case), [1] (Poisson case), [2] (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 $S$.

REFERENCES:
[1] A.S. Cattaneo and G. Felder, Relative formality theorem and quantisation of coisotropic submanifolds, Adv. Math. 208 (2007) 521-548.
[2] 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.
[3] H.V. Lê, Y.-G. Oh, A.G. Tortorella, and L. Vitagliano, Deformations of coisotropic submanifolds in abstract Jacobi manifolds, arXiv:1410.8446.
[4] Y.-G. Oh and J.-S. Park, Deformations of coisotropic submanifolds and strong homotopy Lie algebroids, Invent. Math. 161 (2005) 287--360.