球面稳定同伦群中非平凡元素γ_sξ_n

The Nontrivial Element γ_sξ_n in the Stable Homotopy Groups of Spheres

当p ≥ 5，n ≥ 0 时，（i1i0）＊（hn）∈ExtA^1，pnq（H^＊K，Zp） 在Adams 谱序列中是永久循环，并且收敛到πp^nq-1K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，γshn∈ ExtA^s＋1，t（Zp，Zp） 在Adams谱序列中是永久循环，并且收敛到πt-s-1S中的非零元γsξn，其中p ≥ 7，n ≥ 3 t=p^nq＋sp^2q＋（s-1）pq＋（s-2）q＋s-3，q=2（p-1）.

Let p ≥ 5, n ≥ 0. Then （i1i0）＊（hn） ∈ ExtA^1,p^nq（H^＊K, Zp） is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element in πpnq-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 shn ∈ ExtA^s＋1,t（Zp, Zp） is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element γsξn in πt-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）.