Invariance of the BFV-complex

Abstract

The BFV-formalism was introduced to handle classical systems, equipped with symmetries. It associates a differential graded Poisson algebra to any coisotropic submanifold $S$ of a Poisson manifold $(M,\Pi)$. However the assignment (coisotropic submanifold) $\leadsto$ (differential graded Poisson algebra) is not canonical, since in the construction several choices have to be made. One has to fix: 1. an embedding of the normal bundle $NS$ of $S$ into $M$, 2. a connection $\nabla$ on $NS$ and 3. a special element $\Omega$. We show that different choices of the connection and $\Omega$ -- but with the tubular neighbourhood fixed -- lead to isomorphic differential graded Poisson algebras. If the tubular neighbourhood is changed too, invariance can be restored at the level of germs.