Abstract
In 1981, Cohen constructed an infinite family of homotopy elements ζ k ∈ π*(S) represented by \(h_0 b_k \in Ext_A^{3,2(p - 1)(p^{k + 1} + 1)} (\mathbb{Z}/p,\mathbb{Z}/p)\) in the Adams spectral sequence, where p > 2 and k ⩾ 1. In the paper, we make use of the Adams spectral sequence and the May spectral sequence to prove that the composite map ζ n−1 β 2 γ s+3 is nontrivial in the stable homotopy groups of spheres π t(s,n)−s−8(S), where p ⩾ 7, n > 3, 0 ⩽ s < p − 5 and t(s, n) = 2(p − 1)[p n + (s + 3)p 2 + (s + 4)p + (s + 3)]+s.
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Hong, J., Liu, X. & Zheng, D. On a family involving R.L. Cohen’s ζ-element (II). Sci. China Math. 58, 1745–1752 (2015). https://doi.org/10.1007/s11425-014-4904-1
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DOI: https://doi.org/10.1007/s11425-014-4904-1