σ-相关同伦元素的非平凡性

The Nontriviality of the σ-Related Homotopy Element

本文中,通过几何方法证明了σ相关同伦元素在球面稳定同伦群π_mS中是非平凡的,其中m=p^(n+1)q+2p^nq+(s+3)p^2q+(s+3)pq+(s+3)q-8,p≥7是奇素数,n>3,0≤s<p-3,且q=2(p-1).该σ相关同伦元素在Adams谱序列的E_2-项中由■_s+3■_ng0表示.

In this paper, by geometric method, the a-related homotopy element, which is represented by γ/s＋3lngo in the E2-term of the Adams spectral sequence, will be proved to be nontrivial in the stable homotopy groups of spheres πmS with m = pn＋1q ＋ 2pnq ＋ （s ＋3）p2q＋（s＋3）pq＋（s＋3）q-8, wherep≥ 7 is an odd prime, n〉 3,0≤ s 〈p-3, and q = 2（p - 1）.