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Gelfand-Fuks cohomology

Gel’fand-Fuks cohomology is the cohomology of contionuous alternating chains on the topological algebra of smooth vector fields on smooth manifold, equipped; where the topology on the algebra is given by uniform convergence of all (higher) partial derivative on compacts (sometimes called $C^{\mathrm{\infty }}$-topology on that algebra).

• I. M. Gel'fand, D. B. Fuks, The cohomology of the Lie algebra of vectro fields on a smooth manifold, J. Funct. Analysis 33, 1969, 194–210, II, J. Funct. Anal. 4 (1970) 110-116; The cohomology of the Lie algebra of formal vector fields, Izv. AN SSR 34 (1970), 110-116
• Shigeyuki Morita, Geometry of characteristic classes, Transl. Math. Monographs 199, AMS 2001