An odd vector field Q on a supermanifold M is called homological, if
Q2=0. The operator of Lie derivative LQ​ 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 LQ​ and are represented by Q-invariant tensors made up of the
homological vector field and a symmetric connection on M by means of tensor
operations.Comment: 17 pages, references and comments adde