#### Volume 11, issue 3 (2007)

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Desingularizing homology manifolds

### J Bryant, S Ferry, W Mio and S Weinberger

Geometry & Topology 11 (2007) 1289–1314
##### 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 $f:Y\to X$.

##### Keywords
homology manifold, cell-like map, controlled topology
##### Mathematical Subject Classification 2000
Primary: 57N15, 57P99