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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https://hal-univ-artois.archives-ouvertes.fr/hal-00870098
Contributor : Martintxo Saralegi-Aranguren <>
Submitted on : Friday, October 4, 2013 - 10:27:45 PM
Last modification on : Friday, October 26, 2018 - 10:35:38 AM

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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, Springer Verlag, 1992, 76, pp.21-32. ⟨hal-00870098⟩

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