In mathematics, Gelfand–Fuks cohomology, introduced by Israel Gelfand and Dmitry Fuchs 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 R − {\displaystyle \mathbb {R} -} multilinear alternating forms on the Lie algebra of smooth vector fields where the latter is given the C ∞ {\displaystyle C^{\infty }} topology.
In mathematics, Gelfand–Fuks cohomology, introduced by Israel Gelfand and Dmitry Fuchs 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 R − {\displaystyle \mathbb {R} -} multilinear alternating forms on the Lie algebra of smooth vector fields where the latter is given the C ∞ {\displaystyle C^{\infty }} topology.
Source: Wikipedia "Gelfand–Fuks cohomology" · CC BY-SA 4.0
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