The Mislin genus, phantom maps and classifying spaces
type: Item
instance of: scholarly article
title: The Mislin genus, phantom maps and classifying spaces
zbMATH Open document ID: 0861.55013
DOI: 10.1016/0166-8641(95)00076-3
author: Joseph Roitberg
published in: Topology and its Applications
publication date: 1996-07-03T00:00:00Z
review text: The author shows that the homotopy classes of phantom maps \(\text{Ph}(X,Y)\) and \(\text{Ph}(X',Y)\) are equivalent as sets if \(X\) and \(X'\) are finite type nilpotent spaces with the same genus and \(Y\) has countable higher homotopy groups. He also shows that if \(X\) and \(X'\) have the same genus where \(X\) is simply connected and \(\pi_2X\) is finite, then \(X_\tau\simeq X_\tau'\), where \(X_\tau\) is the fibre of the rationalization map \(X\to X_{(0)}\), and similarly for \(X_\tau'\). This latter result can be used to compute \(\text{Ph}(X,Y)\), where \(X\) has the genus of \(BG\), \(G\) being a simply connected Lie group and \(Y\simeq\Omega^kZ\), \(Z\) being a simply connected finite CW complex.
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55R35
zbMATH DE Number: 896584
zbMATH Keywords: homotopy classes
zbMATH Keywords: phantom maps
zbMATH Keywords: nilpotent spaces
zbMATH Keywords: genus
zbMATH Keywords: homotopy groups
zbMATH Keywords: rationalization
reviewed by: C. S. Hoo
MaRDI profile type: Publication
full work available at URL: 0166-8641(95)00076-3
OpenAlex ID: W2054586220
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description: scientific article; zbMATH DE number 896584