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

作　　者：Xiu Gui LIU 

机构地区：[1]Department of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2007年第3期385-392,共8页数学学报（英文版）

基　　金：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）.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：Stable homotopy of spheres Adams spectral sequence Toda Smith spectrum May spectral sequence 

分 类 号：O187[理学—数学]