On the \(L^ 2\) cohomology of complex spaces
type: Item
instance of: scholarly article
title: On the \(L^ 2\) cohomology of complex spaces
zbMATH Open document ID: 0759.58002
DOI: 10.1007/BF02570851
author: Takeo Ohsawa
published in: Mathematische Zeitschrift
publication date: 1993-03-03T00:00:00Z
full work available at URL: https://eudml.org/doc/174379
review text: 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)].
Mathematics Subject Classification ID: 58A12
Mathematics Subject Classification ID: 14F25
Mathematics Subject Classification ID: 14F40
zbMATH DE Number: 126377
zbMATH Keywords: locally square integrable de Rham cohomology
zbMATH Keywords: reduced complex space
zbMATH Keywords: intersection cohomology
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 126377