A new family in the stable homotopy groups of spheres

Abstract

In this paper, the nontriviality of homotopy elements β 1 ϱ s \beta _1\varrho _s in the p p -primary component of stable homotopy groups of spheres is shown by virtue of the Adams spectral sequence and the May spectral sequence, where ϱ s \varrho _s is represented by b 0 g 0 γ ~ s b_0g_{0}\widetilde {\gamma }_{s} in the Adams spectral sequence, p p is a prime number greater than 5 5 , and 3 ≤ s > p 3\leq s>p .