All Stable Characteristic Classes of Homological Vector Fields

An odd vector field Q on a supermanifold M is called homological, if Q ² = 0. The operator of Lie derivative L _Q makes the algebra of smooth tensor fields on M into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator L _Q and are represented by Q-invariant tensors made up of the homological vector field and a symmetric connection on M by means of the algebraic tensor operations and covariant differentiation.