On some second Hochschild cohomology spaces for algebras of functions on a manifold
This paper deals with the second cohomology group for smooth functions on a manifold. Its main result relies very much on a construction by \textit{H. Omori, Y. Maeda} and \textit{A. Yoshioka} [in Contemp. Math. 179, 213-240 (1994; Zbl 0820.58027)]. It is shown that any continuous 2-cocycle can be written as \(C(u,v)=\delta F(u,v)+B(du,dv)\), where \(F\) is a continuous 1-cochain and \(B\) is a skewsymmetric contravariant 2-tensor on \(M\). The result remains true if ``continuous'' is replaced by a suitable condition of smoothness (goodness). Connected results have been obtained by \textit{G. Pinczon} [Lett. Math. Phys. 39, 143-156 (1997)].
cohomology groups for smooth functions on manifolds
scientific article; zbMATH DE number 989790