Desingularizing homology manifolds

Abstract

We prove that if $X^n$ , $n\ge 6$, is a compact ANR homology $n$–manifold, we can blow up the singularities of $X$ to obtain an ANR homology $n$–manifold with the disjoint disks property. More precisely, we show that there is an ANR homology $n$–manifold $Y$ with the disjoint disks property and a cell-like map $f:Y\to X$.