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Journal Articles Manuscripta mathematica Year : 1992

ℒ2-cohomologie des espaces stratifiésdes espaces stratifiés

Abstract

The first results relating intersection homology with ℒ2-cohomology were found by Cheeger, Goresky and MacPhersson (cf.[4] and [5]). The first spaces considered were the compact stratified pseudomanifolds with isolated singularities. Later, Nagase extended this result to any compact stratified spaceA possessing a Cheeger type riemannian metric μ (cf. [12]). The proof of the isomorphism H∗(2)(A−Σ,μ)≅IHpˉ∗(A) uses the axiomatic caractérisation of the intersection homology of [2]. In this work we 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 in [2]. We also prove that any stratified space possesses a Cheeger type riemannian metric.
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Dates and versions

hal-00870098 , version 1 (04-10-2013)

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  • HAL Id : hal-00870098 , version 1

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Jean-Paul Brasselet, Gilbert Hector, Martintxo Saralegi-Aranguren. ℒ2-cohomologie des espaces stratifiésdes espaces stratifiés. Manuscripta mathematica, 1992, 76, pp.21-32. ⟨hal-00870098⟩
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