On the v_nvarpi_n-related elements in the stable homotopy groups of spheres

摘要

In this paper, we prove the existence of two nontrivial families of homotopy elements b₁ v_nbeta_{1} varpi_{n} and g_s+3v_ngamma_{s}+3varpi_n in the stable homotopy groups of spheres p_*pi_{*} (S), where v_n Î p_{q (pn+2p+1)-3} (S)varpi_n in pi_{q (p^{n}+2p+1)-3} (S) was constructed by X. G. Liu, p is a prime number greater than five, $n geq 4, 0 leq s < p–4, q = 2 (p-1)$n geq 4, 0 leq s < p–4, q = 2 (p-1). The elementary method of proof is by explicit combinatorial analysis of the May spectral sequence.