A Nontrivial Product of Filtration s ＋ 5 in the Stable Homotopy of Spheres A Nontrivial Product of Filtration s + 5 in the Stable Homotopy of Spheres期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A Nontrivial Product of Filtration s ＋ 5 in the Stable Homotopy of Spheres

作者姓名：	Xiu Gui LIU

作者单位：	Department of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China

基金项目：	This paper is supported by the National Natural Science Foundation of China （No. 10501045, 10426028）, the China Postdoctoral Science Foundation and the Fund of the Personnel Division of Nankai University

摘要：	In this paper, some groups Ext A^s.t （Zp, Zp） with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s＋5 in the stable homotopy groups of spheres πpnq＋（s＋3）pq＋（s＋1）q-5S which is represented （up to a nonzero scalar） by β＋2bohh∈ExtA^s＋5,P^nq＋（n＋3）pq＋（n＋1）q＋s（Zp, Zp） in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2（p - 1）.
关键词：	球面稳定同伦非平凡积 σ域流
收稿时间：	15 September 2003
修稿时间：	2003-09-152004-06-28
A Nontrivial Product of Filtration s + 5 in the Stable Homotopy of Spheres

Xiu Gui LIU.A Nontrivial Product of Filtration s + 5 in the Stable Homotopy of Spheres[J].Acta Mathematica Sinica,2007,23(3):385-392.

Authors:	Xiu Gui Liu

Institution:	(1) School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China

Abstract:	In this paper, some groups ${\text{Ext}}^{{s,t}}_{A} {\left( {Zp,Zp} \right)}$ with specialized s and t are first computed by the May spectral sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres $\pi _{{p^{n} q + {\left( {s + 3} \right)}pq + {\left( {s + 1} \right)}q - 5}} S$ which is represented (up to a nonzero scalar) by $\ifmmode\expandafter\tilde\else\expandafter\~\fi{\beta }_{{s + 2}} b_{0} h_{n} \in Ext^{{s + 5,p^{n} q + {\left( {s + 3} \right)}pq + {\left( {s + 1} \right)}q + s}}_{A} {\left( {Z_{p} ,Z_{p} } \right)}$ in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥ 3, 0 ≤ s < p − 3, q = 2(p − 1). This paper is supported by the Youth Project of Tianyuan Foundation of China (No. 10426028), the China Postdoctoral Science Foundation and the Fund of Nankai University Personnel Division

Keywords:	Stable homotopy of spheres Adams spectral sequence Toda Smith spectrum May spectral sequence
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