Topology of homology manifolds (Q1918520)

A long standing problem from geometric topology is solved in this important paper -- now we know that there do exist nonresolvable generalized \(n\)-manifolds \((n\geq 5)\)! In the 1970's geometric topologists were looking for a simple characterization of topological manifolds. The general plan, proposed by \textit{J. W. Cannon} after his successful work on the double suspension problem [ibid. 110, 83-112 (1979; Zbl 0424.57007)], was to take a generalized \(n\)-manifold \(X\) \((n\geq 5)\), find a cell-like resolution \(f:M\to X\) and then, if \(X\) has the disjoint disk property (DDP), shrink the corresponding cell-like decomposition of the topological \(n\)-manifold \(M\). The second step was made possible by the beautiful DDP theorem, proved by \textit{R. D. Edwards} in 1977. Also the first step seemed within reach in (early) 1980's. However, there turned out to be a missing link in the otherwise very powerful resolution theorem, due to \textit{F. S. Quinn} [Mich. Math. J. 34, 285-291 (1987; Zbl 0652.57011)]. This link has now been fixed, but with a twist -- Quinn's local surgery obstruction can be nonzero! The paper under review contains much more and presents a milestone in the history of manifolds theory.