摘要
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.
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.
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)
关键词
科恩
稳定同伦群
家庭
谱序列
亚当斯
π
stable homotopy groups of spheres, Adams spectral sequence, May spectral sequence