A homotopy equivalence that is not homotopic to a topological embedding
type: Item
instance of: scholarly article
title: A homotopy equivalence that is not homotopic to a topological embedding
zbMATH Open document ID: 0923.55008
DOI: 10.1016/S0166-8641(98)00187-4
author: Vo Thanh Liem
author: Yukio Matsumoto
author: G. A. Venema
published in: Topology and its Applications
publication date: 1999-10-25T00:00:00Z
review text: The authors show that for \(n\geq 6\), there is an open subset \(W^n\subset S^n\), such that it is homotopy equivalent to \(S^2\times S^{n-4}\), but there is no compact subset \(X^n\subset W^n\) such that the inclusion \(X^n \to W^n\) is a Čech equivalence. Similarly they obtain that there exists an open subset \(W^4\subset S^4\) such that it is homotopy equivalent to \(S^4\), but there is no compact subset \(X^4\subset W^4\) such that the inclusion \(X^4\to W^4\) is a \(\Check{\text{C}}\)ech equivalence. Using these two results, they construct interesting examples of open manifolds that have unusual compactness properties.
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 57N35
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57N15
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 1307908
zbMATH Keywords: compact subset
reviewed by: Kohhei Yamaguchi
MaRDI profile type: Publication
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full work available at URL: s0166-8641(98)00187-4
OpenAlex ID: W2140896191
description: scientific article; zbMATH DE number 1307908