Batalin-Vilkovisky formalism in the functional approach to classical   field theory
  We develop the Batalin-Vilkovisky formalism for classical field theory on generic globally hyperbolic spacetimes. A crucial aspect of our treatment is the incorporation of the principle of local covariance which amounts to formulate the theory without reference to a distinguished spacetime. In particular, this allows a homological construction of the Poisson algebra of observables in classical gravity. Our methods heavily rely on the differential geometry of configuration spaces of classical fields. 
Klaus Fredenhagen, Katarzyna Rejzner
math-ph gr-qc hep-th math.MP