Deformations of coisotropic submanifolds for fibrewise entire Poisson structures

TL;DR

This paper studies how coisotropic submanifolds deform within fibrewise entire Poisson manifolds, using $L_$-algebras, and explores the extended deformation problem's obstructions.

Contribution

It extends the understanding of deformations of coisotropic submanifolds via $L_$-algebras, including the symplectic case and the analysis of obstructions in extended deformations.

Findings

Deformations are governed by specific $L_$-algebras.

Results recover known symplectic deformation results.

Extended deformation problem is shown to be obstructed.

Abstract

We show that deformations of a coisotropic submanifold inside a fibrewise entire Poisson manifold are controlled by the $L_\infty$-algebra introduced by Oh-Park (for symplectic manifolds) and Cattaneo-Felder. In the symplectic case, we recover results previously obtained by Oh-Park. Moreover we consider the extended deformation problem and prove its obstructedness.