The proper L-S category of Whitehead manifolds
type: Item
instance of: scholarly article
title: The proper L-S category of Whitehead manifolds
zbMATH Open document ID: 1088.55003
published in: Topology and its Applications
publication date: 2006-03-16T00:00:00Z
review text: The main result of the paper states that the proper LS category of an eventually end-irreducible, \(\mathbb{R}^2\)-irreducible Whitehead 3-manifold is 4. Recall that a Whitehead manifold is a contractible open 3-manifold such that any embedded sphere bounds a ball. The manifold is \(\mathbb{R}^2\)-irreducible if any properly embedded plane \(\mathbb{R}^2\subset M\) bounds a half-space \(\mathbb{R}^2\times\mathbb{R}_+\subset M\). For a Whitehead 3-manifold, this is equivalent to \(\varprojlim\,\text{pro\,}\pi_1(X\alpha)= 0\) for any ray \(\alpha: \mathbb{R}_+\to M\). The manifold \(M\) is eventually end-irreducible if there exists an exhausting sequence \(\{M_n\}\) in \(M\) consisting of compact connected submanifolds such that there is \(n_0\) for which each surface \(\partial M\) is incompressible in \(\overline{M- M_{n_0}}\) if \(n> n_0\). This is equivalent to saying that pro-\(\pi_1(X,\alpha)\) is isomorphic to a tower whose bounding homomorphisms are injective.
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 55P57
Mathematics Subject Classification ID: 57N65
zbMATH DE Number: 5012977
zbMATH Keywords: proper homotopy theory
zbMATH Keywords: Lusternik-Schnirelmann category
zbMATH Keywords: Whitehead manifolds
author: Manuel Cárdenas
author: Fernando Muro
author: Antonio Quintero
reviewed by: Yves Félix
MaRDI profile type: Publication
full work available at URL: j.topol.2005.01.031
OpenAlex ID: W2083431710
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DOI: 10.1016/J.TOPOL.2005.01.031
description: scientific article; zbMATH DE number 5012977