Vol. 248, No. 2, 2010

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Invariance of the BFV complex

Florian Schätz

Vol. 248 (2010), No. 2, 453–474

The Batalin–Vilkovisky–Fradkin (BFV) formalism, introduced to handle classical systems equipped with symmetries, associates a differential graded Poisson algebra to any coisotropic submanifold S of a Poisson manifold (M,Π). However, the assignment given by mapping a coisotropic submanifold to a differential graded Poisson algebra is not canonical since in the construction several choices have to be made. One has to fix an embedding of the normal bundle NS of S into M as a tubular neighborhood, a connection on NS, and a special element Ω.

We show that different choices of a connection and an element Ω—but with the tubular neighborhood fixed—lead to isomorphic differential graded Poisson algebras. If the tubular neighborhood is changed as well, invariance can still be restored at the level of germs.

Poisson geometry, coisotropic submanifolds, BFV complex, homological algebra
Mathematical Subject Classification 2000
Primary: 53D17, 55U99
Secondary: 17B60
Received: 14 July 2009
Revised: 12 September 2010
Accepted: 5 October 2010
Published: 1 December 2010

Proposed: Jiang-Hua Lu
Florian Schätz
Center for Mathematical Analysis, Geometry and Dynamical Systems
Departamento de Matematica
Av. Rovisco Pais
1049-001 Lisbon