nLab
Gelfand-Fuks cohomology

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

\infty-Lie theory

∞-Lie theory

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

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 C^\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

Revised on March 22, 2011 22:06:58 by Urs Schreiber (89.204.137.103)