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An isomorphism from intersection homology to \(L_ p\)-cohomology. (English) Zbl 0833.55008
The author concisely recalls singular manifolds, Riemannian pseudomanifolds (the main object of the paper), intersection homology, \(L_p\)-cohomology, and negligible boundary conditions. Then he discusses the cone formula for \(L_p\)-cohomology and shadow forms after J. P. Brasselet, M. Goresky and R. MacPherson [Am. J. Math. 113, No. 6, 1019-1052 (1991; Zbl 0748.55002)]. Using these shadow forms, isomorphism of \(L_p\)-cohomology and intersection homology is proved for conelike structures if \(p\geq 2\). Assuming \(p<2\), the isomorphism holds if the codimension of the singular set is at least \(q\). Finally, the Stokes formulae and the Hodge decomposition for manifolds with negligible boundary is established. The paper involves many references and is intended for specialists.
Reviewer: J.Chrastina (Brno)

55N33 Intersection homology and cohomology in algebraic topology
58A12 de Rham theory in global analysis
58A25 Currents in global analysis
57R65 Surgery and handlebodies
57N80 Stratifications in topological manifolds
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