Intersection homology theory via rectifiable currents (Q1879425)

On a differentiable manifold, there is a representation of ordinary homology theory by so called ``rectifiable currents'' which is a nice setting for variational problems on manifolds see \textit{H. Federer}'s classical book [Geometric mesure theory, New York: Springer Verlag (1969; Zbl 0176.00801)]. Recently much interest has been put on the study of manifolds with singularities. In this case, a natural homology theory is the intersection homology theory introduced by \textit{R. MacPherson} and \textit{M. Goresky} [Topology 19, 135--165 (1980; Zbl 0448.55004), Invent. Math. 72, 77--129 (1983; Zbl 0529.55007)]. What has been achieved in this paper is a rectifiable currents' version of intersection homology theory on stratified pseudomanifolds which provides the foundation for the study of variational problems on manifolds with singularities.