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\(H_{(2)}^* \left( {A - \Sigma ,\mu } \right) \cong IH_*^{\bar p} \left( A \right)\) 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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Brasselet, J.P., Hector, G. & Saralegi, M. ℒ2-cohomologie des espaces stratifiésdes espaces stratifiés. Manuscripta Math 76, 21–32 (1992). https://doi.org/10.1007/BF02567744
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DOI: https://doi.org/10.1007/BF02567744