Intersection of algebraic cycles (Q1356248)

In this expository paper, the author explains with illustrating examples why intersection homology is needed to recover some properties of intersection of cycles and of Poincaré duality both of which fail when one uses the classical homology theory for singular pseudomanifolds. Thereafter he describes the recent results, obtained by the author, together with G. Barthel, K.-H. Fieseler, O. Gabber, and L. Kaup, which are concerned with the existence of associated morphisms in intersection homology and the lifting of algebraic cycles from homology to intersection homology.