Homogeneous ENR's
type: Item
instance of: scholarly article
title: Homogeneous ENR's
zbMATH Open document ID: 0645.57015
DOI: 10.1016/0166-8641(87)90094-0
author: John L. Bryant
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: 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.)
Mathematics Subject Classification ID: 57P05
Mathematics Subject Classification ID: 57P99
zbMATH DE Number: 4052596
zbMATH Keywords: Bing-Borsuk conjecture
zbMATH Keywords: homogeneous
zbMATH Keywords: n-dimensional ENR
zbMATH Keywords: local homology groups
zbMATH Keywords: homology n-manifold
reviewed by: Dušan Repovš
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90094-0
OpenAlex ID: W2083393708
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description: scientific article; zbMATH DE number 4052596