On the \(L^ 2\) cohomology of complex spaces
Let \(X\) be a reduced complex space of pure dimension \(n\) equipped with a Hermitian metric. It is proved that the \(L^ 2_{\text{loc}}\) (i.e. locally square integrable) de Rham cohomology group of \(X\) is canonically isomorphic to the (middle) intersection cohomology group of \(X\). This settles a question of \textit{J. Cheeger}, \textit{M. Goresky} and \textit{R. MacPherson} [cf. Ann. Math. Stud. 102, 303-340 (1982; Zbl 0503.14008)].
locally square integrable de Rham cohomology
scientific article; zbMATH DE number 126377
scientific article