Homogeneous ENR's
The following result is proved: Theorem. Let X be a homogeneous, n- dimensional ENR and suppose that the local homology groups \(H_*(X,X- \{x\};{\mathbb{Z}})\) (x\(\in X)\) are finitely generated. Then X is a homology n-manifold. (Reviewer's remarks: The author apparently wasn't aware of a more general result proved by \textit{G. E. Bredon} earlier [Topology of manifolds, Proc. Univ. Georgia 1969, 461-469 (1971; Zbl 0311.57008)] to the effect that, for a countable PID R, every locally compact metrizable space X that is homologically locally connected with respect to R and has finite cohomological dimension with respect to R, is a homology manifold over R provided that for each pair of points x,y\(\in X\) and each integer k, the modules \(H_ k(X,X-\{x\};R)\) and \(H_ k(X,X-\{y\};R)\) are isomorphic and finitely generated. Nevertheless, Bryant's proof is interesting because it employs methods completely different from those of Bredon.)
scientific article; zbMATH DE number 4052596
scientific article