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 the algebraic tensor operations and covariant differentiation.
- characteristic classes
- gauge theories
ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics