Cohomology of the variational complex in BRST theory

We show that cohomology of the variational complex in field-antifield BRST theory on an arbitrary manifold is equal to the de Rham cohomology of this manifold.Comment: 17 page

Covariant Spin Structure

Every Dirac spin structure on a world manifold is associated with a certain gravitational field, and is not preserved under general covariant transformations. We construct a composite spinor bundle such that any Dirac spin structure is its subbundle, and this bundle admits general covariant transformations.Comment: 26 pages, LaTe