球面稳定同伦群中非平凡元素γ_sξ_n

当p≥5, n≥0时,(i_1i_0)_*(h_n)∈Ext_■~(1,p~nq)(H~*K,Z_p)在Adams谱序列中是永久循环,并且收敛到π_(p~nq-1)K中的非零元.本文在此基础上,考虑了涉及第三希腊字母类乘积元素的收敛性,并且扩大了球面稳定同伦群中非平凡元素滤子s+1的取值范围,即当p+1 s+1 2p时,■_sh_n∈Ext_■~(s+1,t)(Z_p,Z_p)在Adams谱序列中是永久循环,并且收敛到π_(t-s-1)S中的非零元γ_sξ_n,其中p≥7, n≥3, t=p~nq+sp~2q+(s-1)pq+(s-2)q+s-3,q=2(p-1).

The Nontrivial Element γsξn in the Stable Homotopy Groups of Spheres

Let p ≥ 5, n ≥ 0. Then (i₁i₀)_*(h_n) ∈ Ext_A^1,pnq(H^*K, Z_p) is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element in π_pⁿq-1K. Based on this result, we consider the convergence of the product involving the third Greek letter family element and expand the filtration s + 1 of the nontrivial element in π_*S. In other words, we prove that_sh_n ∈ Ext_A^s+1,t(Z_p, Z_p) is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element γ_sξ_n in π_t-s-1S, for p + 1 < s + 1 < 2p, where p ≥ 7, n ≥ 3, t=pⁿq + sp²q + (s -1)pq + (s -2)q + s -3, q=2(p -1).