Gelfand–Fuks cohomology

In mathematics, Gelfand–Fuks cohomology, introduced in (Gel'fand & Fuks 1969–70), is a cohomology theory for Lie algebras of smooth vector fields.

It differs from the Lie algebra cohomology of Chevalley-Eilenberg in that its cochains are taken to be continuous multilinear alternating forms on the Lie algebra of smooth vector fields where the latter is given the

∞

{\displaystyle C^{\infty }}

topology.