Homology \(n\)-spheres as codimension-\((n+1)\) shape m\(_{\text{simpl}}\)-fibrators
type: Item
instance of: scholarly article
title: Homology \(n\)-spheres as codimension-\((n+1)\) shape m\(_{\text{simpl}}\)-fibrators
zbMATH Open document ID: 1148.57031
author: Violeta Vasilevska
published in: Topology and its Applications
publication date: 2008-06-19T00:00:00Z
review text: Let \(N\) be a closed, orientable, PL \(n\)-manifold such that every \(f:N\to N\) inducing a \(\pi_1\)-isomorphism is a homotopy equivalence; every epimorphism \(\pi_1(N)\to\pi_1(N)\) is an isomorphism; \(H_i(N)=0\) for \(0<i<k-1\leq n\) for some \(k>2\). Then \(N\) is a codimension-\(k\) shape m\(_{\text{simpl}}\)-fibrator, i.e. every \(N\)-shaped PL map \(p:M\to B\), \(M\) a closed PL \((n+k)\)-manifold and \(B\) a simplicial triangulated \(k\)-manifold, is an approximate fibration.
reviewed by: David B. Gauld
Mathematics Subject Classification ID: 57N15
Mathematics Subject Classification ID: 55R65
Mathematics Subject Classification ID: 57N25
Mathematics Subject Classification ID: 54B15
zbMATH DE Number: 5290944
zbMATH Keywords: approximate fibration
zbMATH Keywords: shape fibrator
zbMATH Keywords: Hopfian manifold
zbMATH Keywords: manifold homotopically determined by \(\pi_1\)
MaRDI profile type: Publication
full work available at URL: j.topol.2008.01.011
OpenAlex ID: W2071830419
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DOI: 10.1016/J.TOPOL.2008.01.011
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description: scientific article; zbMATH DE number 5290944