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We construct sheaf-cohomological analogues of Mathai-Quillen forms, that is,holomorphic bundle-valued differential forms whose cohomology classes areindependent of certain deformations, and which are believed to possessThom-like properties. Ordinary Mathai-Quillen forms are special cases of theseconstructions, as we discuss. These sheaf-theoretic variations arise physicallyin A/2 and B/2 pseudo-topological field theories, and we comment on theirorigin and role.

Analogues of Mathai-Quillen forms in sheaf cohomology and applications to topological field theory