The Gottlieb group of a wedge of suspensions. (English) Zbl 1314.55009

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 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.


55Q20 Homotopy groups of wedges, joins, and simple spaces


Zbl 0185.27102
Full Text: DOI Euclid


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