nLab Gelfand-Fuks cohomology

Examples

$\infty$-Lie algebras

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

• I. M. Gel'fand, D. B. Fuks, The cohomology of the Lie algebra of vector 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

Last revised on August 24, 2015 at 01:47:36. See the history of this page for a list of all contributions to it.