Non cell like decompositions of \(S^ 3\)
type: Item
instance of: scholarly article
title: Non cell like decompositions of \(S^ 3\)
zbMATH Open document ID: 0552.55016
author: D. S. Coram
author: P. F. jun. Duvall
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The authors consider two classes of maps, \(f: S^ 3\to X\), from the 3- sphere to a compactum X. The first class consists of maps that are non- constant approximate fibrations whose fiber is a pointed FANR. They establish that either f factors as \(f=pg\) where \(p: Y\to X\) is a covering map and g is cell like or f can be approximated by maps topologically equivalent to the Hopf fibration. The second class consists of maps with the property that \(f^{-1}(x)\) has the shape of a circle for each \(x\in X\). For such maps they establish that if X is an ANR and each point inverse links some other point inverse, then \(X\approx S^ 2\). [Recently, the reviewer and \textit{R. J. Daverman} have extended this analysis and removed both the assumption that X is an ANR and that point inverses link; see Trans. Am. Math. Soc. 288, 273-291 (1985).]
Mathematics Subject Classification ID: 55R65
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 54C56
Mathematics Subject Classification ID: 54C55
zbMATH DE Number: 3879730
zbMATH Keywords: cell like map
zbMATH Keywords: maps with fibre of the shape of a circle
zbMATH Keywords: non-constant approximate fibrations
zbMATH Keywords: covering map
zbMATH Keywords: Hopf fibration
MaRDI profile type: Publication
full work available at URL: pjm.1984.115.47
OpenAlex ID: W2089168584
DOI: 10.2140/PJM.1984.115.47
description: scientific article; zbMATH DE number 3879730