On the contact cohomology of isolated hypersurface singularities
Let \(U\) be an open set in \(C^ N\), \(0\in U\), \(f: (U,0)\to (R,0)\) be a \(C^ \infty\)-function, \(F\) corresponds to the \(k\)-truncated Taylor expansion of \(f\) in the structure sheaf of the \(k\)-th infinitesimal neighborhood of \(U\). The author describes cohomologies of the complex \[ \Lambda^ ._{f,k-\cdot}: \Lambda^ 0_{f,k} @>{\mathcal D} >>\dots \to \Lambda^ p_{f,k-p} @>{\mathcal D} >> \Lambda^{p+1}_{f,k-p-1}\to \dots, \qquad \text{where} \qquad \Lambda^ p_{f,k-p}= {{\Omega^ p_{f,k-p,0}} \over {F\Omega^ p_{f,k-p,0}}} \] in notations of the author [Math. Ann. 262, 255-272 (1983; Zbl 0507.58013); Chin. Ann. Math., Ser. A 12, No. 2, 137-144 (1991; Zbl 0735.32023)].
scientific article; zbMATH DE number 482129