In mathematics, Gelfand–Fuks cohomology, introduced by Israel Gelfand and Dmitry Fuchs in , 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 topology.
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