Homology of stratified spaces (Q2704629)

\textit{R. M. Goresky} [Trans. Am. Math. Soc. 267, 175-196 (1981; Zbl 0476.57019)] proved that the ordinary integral singular homology of a smooth manifold \(X\) is isomorphic to the cobordism group based on embedded compact oriented Whitney stratified subsets of \(X\). In the same paper, Goresky pointed out that such a result might be true for any Whitney stratified object \(X\). While the authors of the paper under review do not solve this open problem for Whitney stratifications, they do announce analogous results for two other types of stratified spaces: the abstract stratified sets in [\textit{J. Mather}, Notes on topological stability (Harvard Univ. mimeographed notes, Cambridge) (1970)] and the (c)-regular stratified spaces in [\textit{K. Bekka}, ``Singularity theory and its applications'', Lect. Notes Math. 1462, 42-62 (1991; Zbl 0733.58003)].