A ϖ _n-Related Family of Homotopy Elements in the Stable Homotopy of Spheres

Abstract

To determine the stable homotopy groups of spheres π _*(S) is one of the central problems in homotopy theory. Let p be a prime greater than 5. The authors make use of the May spectral sequence and the Adams spectral sequence to prove the existence of a ϖ _n-related family of homotopy elements, β ₁ ω _n γ _s, in the stable homotopy groups of spheres, where n > 3, 3 ≤ s < p − 2 and the ϖ _n-element was detected by X. Liu.

Keywords

Stable homotopy groups of spheres / Adams spectral sequence / May spectral sequence

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