The Gottlieb group of a wedge of suspensions
type: Item
instance of: scholarly article
title: The Gottlieb group of a wedge of suspensions
zbMATH Open document ID: 1314.55009
author: Martin Arkowitz
author: Ken-ichi Maruyama
published in: Journal of the Mathematical Society of Japan
publication date: 2014-09-30T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jmsj/1406206970
review text: Let \(X\) be a connected space and \(\pi_n(X)\) its \(n\)-th homotopy group. The Gottlieb groups \(G_n(X)\subseteq \pi_n(X)\) were introduced and studied by \textit{D. H. Gottlieb} [Am. J. Math. 91, 729--756 (1969; Zbl 0185.27102)] and have been shown to have many topological applications. The authors study \(G_n(\Sigma X_1\vee\cdots\vee \Sigma X_k)\), where \(\Sigma X_i\) is the suspension of the space \(X_i\) for \(i=1,\ldots, k\) with particular attention to the case \(k=2\) and \(X_i\) a sphere. Necessary and sufficient conditions for an element of \(\pi_n(\Sigma X_1\vee\cdots\vee \Sigma X_k)\) to be in \(G_n(\Sigma X_1\vee\cdots\vee \Sigma X_k)\) are presented and \(G_n(M(A,n))\) for some Moore spaces \(M(A,n)\) is computed.
reviewed by: Marek Golasiński
Mathematics Subject Classification ID: 55Q20
zbMATH DE Number: 6350038
zbMATH Keywords: homotopy group
zbMATH Keywords: Gottlieb group
zbMATH Keywords: wedge sum
zbMATH Keywords: Hopf invariant
zbMATH Keywords: Whitehead product
MaRDI profile type: Publication
OpenAlex ID: W2081537384
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cites work: Q4192669
DOI: 10.2969/JMSJ/06630735
description: scientific article; zbMATH DE number 6350038