  We construct sheaf-cohomological analogues of Mathai-Quillen forms, that is,
holomorphic bundle-valued differential forms whose cohomology classes are
independent of certain deformations, and which are believed to possess
Thom-like properties. Ordinary Mathai-Quillen forms are special cases of these
constructions, as we discuss. These sheaf-theoretic variations arise physically
in A/2 and B/2 pseudo-topological field theories, and we comment on their
origin and role.
