On a family involving R.L. Cohen's ζ-element(II)  

作　　者：HONG JianGuo LIU XiuGui ZHENG Da 

机构地区：[1]School of Mathematical Sciences and LPMC, Nankai University

出　　处：《Science China Mathematics》2015年第8期1745-1752,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11071125,11261062 and 11171161);Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20120031110025);the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry(Grant No.2012940)

摘　　要：In 1981, Cohen constructed an infinite family of homotopy elements ζk∈ π＊（S） represented by h0bk ∈ ExtA3,2（p-1）（pk＋1＋1）（z/p,Z/p） in the Adams spectral sequence, where p 〉 2 and k ≥ 1. In this paper, we make use of the Adams spectral sequence and the May spectral sequence to prove that the composite map ζn-1β2γs＋3 is nontrivial in the stable homotopy groups of spheres πt（s,n）-s-8（S）, where p ≥7, n 〉 3, 0≤s 〈p-5 andt（s,n） =2（p-1）[pn＋（s＋3）p2＋（s＋4）p＋（s＋3）]＋s.In 1981, Cohen constructed an infinite family of homotopy elements ζk∈π*(S) represented by h0bk∈ Ext3,2(p-1)(pk+1+1)A(Z/p, Z/p) in the Adams spectral sequence, where p > 2 and k≥1. In this paper,we make use of the Adams spectral sequence and the May spectral sequence to prove that the composite map ζn-1β2γs+3is nontrivial in the stable homotopy groups of spheres πt(s,n)-s-8(S), where p≥7, n > 3,0≤s < p- 5 and t(s, n) = 2(p- 1)[pn+(s + 3)p2 +(s + 4)p +(s + 3)] + s.

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

分 类 号：O152[理学—数学]