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Pseudomanifolds with a metric on the nonsingular part are considered. Let^? be the largest perversity strictly smaller then ~. Under the assumption of concordance of a metric with the conelike structure there is an isomorphism of Lp-cohomology and intersection homology for/? > 2. We prove this isomorphism using shadow forms. For/? < 2 we need to assume that the codimension of the singular set Σ is at least q, where ^ + ^ = l. We investigate a negligible boundary condition. It is equivalent to the vanishing of intersection homology groups of links in dimensions about ^ (/ is the dimension of a link). On the sheaf level it is equivalent to codim(Z) > max(/?, q) and the sheaf J*?(p) = /C? is dual to ̂ = /C? in the sense of Verdier. 1991 Mathematics Subject Classification: 55N33, 58A12; 57R65, 58A25. 0 Introduction The purpose of this paper is to present a connection between the intersection homology theory and Lp-cohomology. We investigate the simplest case: Riemannian pseudomanifolds. These are piecewise linear singular spaces with a Riemannian metric on the nonsingular part which is concordant with a triangulation. (For precise definitions see §§1-3.) We show that there exists a perversity (the maximal smaller then i/p) such that intersection homology with respect to this perversity and Lp-cohomology coincide. It's a Version of the de Rham isomorphism. The condition of Lp-growth in the neighborhood of singularities for forms corresponds to restrictions for intersections of chains with singular strata. To produce an explicit geometric isomorphism we use shadow forms (§13). This isomorphism was suggested by the authors of [BGM]. Recently an abstract isomorphism was obtained by B. Youssin [Y]. Next we consider an important functional condition of a negligible * Partially supported by KBN 2 1139 91 01

An isomorphism from intersection homology to L p -cohomology