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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)

##### MSC:
 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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