A ϖn-Related Family of Homotopy Elements in the Stable Homotopy of Spheres

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.