关键词: stable homotopy of spheres, Adams spectral sequence, Smith Toda spectrum

Abstract:

This study proves a general result on convergence of  α₂ x ∈ Ext_A^{s+2, tq+2q+1}(Z_p, Z_p) in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres π_tq+2q-4S which is represented in the Adams spectral sequence by α₂f_n, α₂f'_n^, ，α₂h_uh_mh_n ∈ Ext_A^{5, tq+2q+1}(Z_p, Z_p) with tq = p^n+1q+2pⁿq, 2pⁿ⁺¹q+pⁿq, p^uq+p^mq+pⁿq, respectively, where α₂ ∈Ext_a^{2, 2q+1}Z_p, Z_p), f_n ∈ Ext_A3, ^_pn+1q+2pⁿq(Z_p, Z_p), f'_n ∈ Ext_A3, 2pⁿ⁺¹q+pⁿq (Z_p, Z_p), h_n ∈ Ext_A1,pⁿq(Z_p, Z_p) and p ≥ 5 is a prime, q = 2(p-1), n ≥ 2.

Key words: stable homotopy of spheres, Adams spectral sequence, Smith Toda spectrum