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Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces pp 1–48Cite as

Gottlieb Groups of Spheres

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Abstract

This 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.

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  1. Institute of Mathematics, Casimir the Great University, Bydgoszcz, Poland

    Marek Golasiński

  2. Shinshu University, Matsumoto, Nagano, Japan

    Juno Mukai

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  1. Marek Golasiński
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Golasiński, M., Mukai, J. (2014). Gottlieb Groups of Spheres. In: Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces. Springer, Cham. https://doi.org/10.1007/978-3-319-11517-7_1

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