\(\mathcal L^ 2\)-cohomologie des espaces stratifiés. (\(\mathcal L^ 2\)- cohomology of stratified spaces)
The first results relating intersection homology with \({\mathcal L}^ 2\)- cohomology were found by \textit{J. Cheeger} [Proc. Symp. Pure Math. 36, 91- 146 (1980; Zbl 0461.58002)] and by \textit{J. Cheeger}, \textit{M. Goresky} and \textit{R. MacPherson} [Ann. Math. Stud. 102, 303-340 (1982; Zbl 0503.14008)], in the case of compact stratified pseudomanifolds with isolated singularities. Using the axiomatic characterization of the intersection homology, \textit{M. Nagase} [Adv. Stud. Pure Math. 8, 273-279 (1987; Zbl 0625.55001)] extended the study of any compact stratified space \(A\) possessing a Cheeger type Riemannian metric \(\mu\) and he proved the isomorphism \(H_{(2)}^*(A-\Sigma,\mu)\cong IH_ *^{\bar p}(A)\). In this work the authors show how to realize this isomorphism by the usual integration of differential forms on simplices. The main tool used is the blow up of \(A\) into a smooth manifold, introduced by the authors [Ann. Global Anal. Geom. 9, No. 3, 211-243 (1991; Zbl 0702.57003)]. They also prove that any stratified space possesses a Cheeger type Riemannian metric.
scientific article; zbMATH DE number 97880
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