ℒ2-cohomologie des espaces stratifiésdes espaces stratifiés

International audienceThe 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