A note on Hempel--McMillan coverings of 3-manifolds
type: Item
instance of: scholarly article
title: A note on Hempel--McMillan coverings of 3-manifolds
zbMATH Open document ID: 1139.57011
published in: Topology and its Applications
publication date: 2007-04-18T00:00:00Z
review text: The paper provides a new proof, as well as a slight generalization, of a result of [\textit{J. P. Hempel} and \textit{D. R. McMillan jun.}, Fundam. Math. 64, 99--104 (1969; Zbl 0176.53302)], saying that a closed \(3\)-manifold which is a union of three open \(n\)-punctured balls (\(n\geq 0\)) must be a connected sum of \(S^3\) and \(S^2\)-bundles over \(S^1\). The facts are reinterpreted from the point of view of the notion of \(A\)-category due to [\textit{M. Clapp} and \textit{D. Puppe}, Trans. Am. Math. Soc. 298, 603--620 (1986; Zbl 0618.55003)]. When \(A\) is a point, this is just the classical Lusternik-Shnirelmann category. The authors are concerned here with the case that \(A\) is a point or the \(2\)-sphere \(S^2\).
reviewed by: D. Matei
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 55M30
zbMATH DE Number: 5144523
zbMATH Keywords: Lusternik-Schnirelmann category
zbMATH Keywords: coverings of \(3\)-manifolds by open subsets
author: J. C. Gómez-Larrañaga
author: F. González-Acuña
author: Wolfgang Heil
MaRDI profile type: Publication
full work available at URL: j.topol.2006.04.022
OpenAlex ID: W2080810595
cites work: Invariants of the Lusternik-Schnirelmann Type and the Topology of Critical Sets
cites work: Lusternik-Schnirelmann category of 3-manifolds
cites work: 3-manifolds that are covered by two open bundles
cites work: Higher dimensional manifolds with \(S ^{1}\)-category 2
cites work: Seifert unions of solid tori
cites work: Q4134602
cites work: Covering three-manifolds with open cells
DOI: 10.1016/J.TOPOL.2006.04.022
description: scientific article; zbMATH DE number 5144523