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\begin{document}

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\section*{Gelfand-Fuks cohomology}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{cohomology}{}\paragraph*{{Cohomology}}\label{cohomology}

[[!include cohomology - contents]]

\hypertarget{lie_theory}{}\paragraph*{{$\infty$-Lie theory}}\label{lie_theory}

[[!include infinity-Lie theory - contents]]

\textbf{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).

\begin{itemize}%
\item [[I. M. Gel'fand]], D. B. Fuks, \emph{The cohomology of the Lie algebra of vector fields on a smooth manifold}, J. Funct. Analysis \textbf{33}, 1969, 194--210, II, J. Funct. Anal. \textbf{4} (1970) 110-116; \emph{The cohomology of the Lie algebra of formal vector fields}, Izv. AN SSR 34 (1970), 110-116
\item Shigeyuki Morita, \emph{Geometry of characteristic classes}, Transl. Math. Monographs 199, AMS 2001

\end{itemize}
[[!redirects Gel'fand-Fuks cohomology]] [[!redirects Gelfand-Fuchs cohomology]]



\end{document}