Deformations of Coisotropic Submanifolds in Jacobi Manifolds

Abstract

In this paper, we attach an $L_{\infty }$-algebra to any coisotropic submanifold in a Jacobi manifold. Our construction generalizes and unifies analogous constructions by Oh-Park (symplectic case), Cattaneo-Felder (Poisson case), Lê-Oh (locally conformal symplectic case). As a new special case, we attach an $L_{\infty }$-algebra to any coisotropic submanifold in a contact manifold. The $L_{\infty }$-algebra of a coisotropic submanifold $S$ governs the (formal) deformation problem of $S$.

arXiv comment41 pages, v2: several revisions, title and abstract slightly changed, mathematics unchanged; final version, to appear in J. Sympl. Geom. 16 (2018)