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A note on products in stable homotopy groups of spheres via the classical Adams spectral sequence. (English) Zbl 1458.55009

The determination of the stable homotopy group of spheres \(\pi_*(S^0)\) is important in stable homotopy theory. For given prime \(p\), the classical Adams spectral sequence and Adams-Novikov spectral sequence are effective tools to detect the \(p\)-component of \(\pi_*(S^0)\). To compute the Adams spectral sequence, there is the May spectral sequence which converges to the \(E_2\) term of the Adams spectral sequence. Using the above spectral sequences, the authors show that many product elements are non-trivial in \(\pi_*(S^0)\) and the stable homotopy group of the Smith-Toda spectrum. For details, see the main Theorem 1.1. These new results cover and extend most of the results obtained by Liu and his collaborators [X. Liu, Arch. Math. 91, No. 5, 471–480 (2008; Zbl 1155.55005)].

MSC:

55Q45 Stable homotopy of spheres
55T15 Adams spectral sequences

Citations:

Zbl 1155.55005
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