A NON-TRIVIAL PRODUCT OF FILTRATION s+6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES  

作　　者：赵浩 刘秀贵 金应龙 

机构地区：[1]School of Mathematical Sciences,Nankai University [2]School of Mathematical Sciences and LPMC,Nankai University [3]Department of Mathematics,Tianjin University

出　　处：《Acta Mathematica Scientia》2009年第2期276-284,共9页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (10501045, 10771105);the NCET and the Fund of the Personnel Division of Nankai University.

摘　　要：By a method improving that of [1], the authors prove the existence of a non-trivial product of filtration, s ＋ 6, in the stable homotopy groups of sphere, πt-6S, which is represented up to non-zero scalar by β^-s＋2ho（hmbn-1 -hnbm-1） ∈ ExtA^s＋6,t＋s（Zp, Zp） in the Adams spectral sequence, where p ≥ 7, n ≥ m ＋ 2 ≥ 5, q = 2（p- 1）, 0 ≤ s 〈 p - 2, t= （s ＋ 2 ＋ （s ＋ 2）p ＋ p^m ＋ p^n）q. The advantage of this method is to extend the range of s without much complicated argument as in [1].By a method improving that of [1], the authors prove the existence of a non-trivial product of filtration, s ＋ 6, in the stable homotopy groups of sphere, πt-6S, which is represented up to non-zero scalar by β^-s＋2ho（hmbn-1 -hnbm-1） ∈ ExtA^s＋6,t＋s（Zp, Zp） in the Adams spectral sequence, where p ≥ 7, n ≥ m ＋ 2 ≥ 5, q = 2（p- 1）, 0 ≤ s 〈 p - 2, t= （s ＋ 2 ＋ （s ＋ 2）p ＋ p^m ＋ p^n）q. The advantage of this method is to extend the range of s without much complicated argument as in [1].

关 键 词：Stable homotopy groups of spheres Adams spectral sequence May spectral sequence 

分 类 号：O152[理学—数学]