Abstract
AbstractThis chapter published in [20] takes up the systematic study of the Gottlieb groups \(G_{n+k}(\mathbb{S}^{n})\) of spheres for k ≤ 13 by means of the classical homotopy theory methods. We fully determine the groups \(G_{n+k}(\mathbb{S}^{n})\) for k ≤ 13 except for the two-primary components in the cases: \(k = 9,n = 53;k = 11,n = 115\). Especially, we show that \([\iota _{n},\eta _{n}^{2}\sigma _{n+2}] = 0\) if \(n = 2^{i} - 7\) for i ≥ 4.KeywordsGottlieb GroupToda BracketCoextensionHomotopy GroupsCofiber SequenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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