σ-相关同伦元素的非平凡性
The Nontriviality of the \sigma-Related Homotopy Element
Received: April 11, 2016  Revised: July 07, 2017
DOI：10.16205/j.cnki.cama.2018.0024

 Author Name Affiliation E-mail WANG Yu College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China. wdoubleyu@aliyun.com
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本文中, 通过几何方法证明了$\sigma$相关同伦元素在球面稳定同伦群$\pi_{m}S$中是非平凡的, 其中 $m=p^{n+1}q+2p^{n}q+(s+3)p^{2}q+(s+3)pq+(s+3)q-8,~p\geqslant 7$是奇素数, $n>3$, $0\leqslant s < p-3$, 且$q=2(p-1)$. 该$\sigma$相关同伦元素在Adams谱序列的 $E_2${-}项中由$\widetilde{\gamma} _{s+3}\widetilde{l}_{n}g_{0}$表示.
In this paper, by geometric method, the $\sigma$-related homotopy element, which is represented by $\widetilde{\gamma}_{s+3}\widetilde{l}_{n}g_{0}$ in the $E_2$-term of the Adams spectral sequence, will be proved to be nontrivial in the stable homotopy groups of spheres $\pi_{m}S$ with $m=p^{n+1}q+2p^{n}q+(s+3)p^{2}q+(s+3)pq+(s+3)q-8$, where $p\geqslant 7$ is an odd prime, $n>3$, $0\leqslant s < p-3$, and $q=2(p-1)$.