关键词: Stable homotopy groups of spheres, Adams spectral sequence, May spectral sequence

Abstract:

By a method improving that of [1], the authors prove the existence of a nontrivial troduct of filtration, s + 6, in the stable homotopy groups of sphere, Π_t−6S, which is represented up to non-zero scalar by β_s+2h₀(h_mb_n−1 −h_nb_m−1) ∈ Ext^s+6,t+s_A (Z_p, Z_p) in the Adams spectral sequence, where p ≥ 7, n ≥ _m + 2 ≥ 5, q = 2(p − 1), 0 ≤ s < p − 2, t= (s + 2+ (s + 2)p + p^m + pⁿ)q. The advantage of this method is to extend the range of s without much complicated argument as in [1].

Key words: Stable homotopy groups of spheres, Adams spectral sequence, May spectral sequence