Deformations of Coisotropic Submanifolds in Jacobi Manifolds

TL;DR

This paper constructs an $L_infty$-algebra for coisotropic submanifolds in Jacobi manifolds, unifying various geometric cases and governing their deformation theory.

Contribution

It introduces a unified $L_infty$-algebra framework for coisotropic submanifolds in Jacobi manifolds, extending previous constructions to contact manifolds.

Findings

Unified $L_infty$-algebra for Jacobi, contact, symplectic, and Poisson cases

Provides a formal deformation theory for coisotropic submanifolds

Generalizes existing geometric deformation frameworks

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), L\^e-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 $S$.