Journal of Symplectic Geometry

Volume 16 (2018)

Number 4

Deformations of coisotropic submanifolds in Jacobi manifolds

Pages: 1051 – 1116



Hong Vân Lê (Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic)

Yong-Geun Oh (Center for Geometry and Physics, Institute for Basic Sciences (IBS), Pohang, South Korea; and Department of Mathematics, POSTECH, Pohang, South Korea)

Alfonso G. Tortorella (Dipartimento di Matematica e Informatica, Università degli Studi di Firenze, Italy)

Luca Vitagliano (Dipartimento di Matematica, Università degli Studi di Salerno, Fisciano, Salerno, Italy)


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), and 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 $S$.

The first-named author is partially supported by RVO: 67985840.

The second-named author is supported by the IBS project #IBS-R003-D1.

Received 29 July 2015

Accepted 9 January 2018

Published 11 February 2019