| 王玉玉.σ-相关同伦元素的非平凡性[J].数学年刊A辑,2018,39(3):273~286 |
| 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 |
| 中文关键词: 球面稳定同伦群, 球谱, Adams谱序列, May谱序列 |
| 英文关键词:Stable homotopy groups of spheres, Sphere spectrum, Adams spectral sequence, May spectral sequence |
| 基金项目:本文受到国家自然科学基金 (No.11301386) 的资助. |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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 $q=2(p-1)$. |
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