Homotopy truncations of homotopically stratified spaces

Intersection homology of Goresky and MacPherson can be defined from theDeligne sheaf, obtained from truncations of complexes of sheaves. Asintersection homology is not the homology of a particular space, the search fora family of spaces whose homologies have properties analogous to intersectionhomology has developed. For some stratified spaces, M. Banagl has introducedsuch a family by using a topological truncation: the original link is replacedby a truncation of its homological Moore resolution. In this work, we study the dual approach in the Eckmann-Hilton sense : weconsider the stratified space obtained by replacing the original link by aPostnikov approximation. The main result is that our construction restores thespace constructed by Gajer to establish an intersection Dold-Thom theorem. We are conducting this study within the general framework of Quinn'shomotopically stratified spaces.