Jacobi bundles and the BFV-complex

TL;DR

This paper extends the BFV-complex construction from Poisson to Jacobi manifolds, including contact and l.c.s. cases, to control coisotropic deformation problems under various equivalences.

Contribution

It introduces a generalized BFV-complex framework applicable to Jacobi manifolds, broadening the scope from Poisson settings.

Findings

BFV-complex constructed for Jacobi manifolds

Controls coisotropic deformation under Hamiltonian and Jacobi equivalence

Applicable to contact and l.c.s. geometries

Abstract

We extend the construction of the BFV-complex of a coisotropic submanifold from the Poisson setting to the Jacobi setting. In particular, our construction applies in the contact and l.c.s. settings. The BFV-complex of a coisotropic submanifold $S$ controls the coisotropic deformation problem of $S$ under both Hamiltonian and Jacobi equivalence.