Wedge cancellation of certain mapping cones. (English) Zbl 0744.55008

The author proves the following Theorem. Let \(p\) be a fixed prime integer. Given \(f_ i,g_ j:S^{4n-1}_{(p)}\to \vee^ kS^{2n}_{(p)}\), \(1\leq i\leq H\), \(1\leq j\leq M\), assume that they represent elements in \(\pi_{4n-1}(\vee^ kS^{2n})_{(p)}\) of infinite order if \(i\leq m\), \(j\leq m'\), and elements of finite order if \(i>m\), \(j>m'\). Then \(\bigvee^ H_{i=1}C_{f_ i}\simeq \bigvee^ M_{j=1}C_{g_ j}\) if and only if: (i) \(H=M\), \(m=m'\); (ii) \(\bigvee^ H_{i=m+1}C_{f_ i}\simeq \bigvee^ H{j=m+1}C_{g_ j}\);
(iii) \(C_{f_{\sigma(j)}}\simeq C_{g_ j}\), \(j=1,\dots,m\), for some permutation \(\sigma\) of \(\{1,2,\dots,m\}\).
Reviewer: M.Mimura (Okayama)


55Q20 Homotopy groups of wedges, joins, and simple spaces
55P15 Classification of homotopy type
Full Text: Numdam EuDML


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