Intersection homology and Poincaré duality on homotopically stratified spaces (Q1022517)

The paper under review shows that intersection homology extends Poincaré duality to spaces stratified by manifolds and satisfying additional homotopy conditions on the ``gluing''. The author uses a modified version of \textit{F. Quinn}'s definition [J. Am. Math. Soc. 1, 441--499 (1988; Zbl 0655.57010)] of such spaces, which he calls manifold homotopically stratified spaces (MHSSs). As an important step towards establishing Poincaré duality for MHSSs the author proves that the sheaf complex of their singular intersection chains is quasi-isomorphic to the Deligne sheaf complex, stating that ``the main proof techniques involve blending the global algebraic machinery of sheaf theory with local homotopy calculations''. The paper is clearly structured and well written.