数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (2): 276-284.doi: 10.1016/S0252-9602(09)60028-X

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

 赵浩, 刘秀贵, 金应龙   

  1. School of Mathematical Sciences, Nankai University, Tianjin 300071, China
  • 收稿日期:2006-06-13 修回日期:2007-03-05 出版日期:2009-03-20 发布日期:2009-03-20
  • 基金资助:

    This research is partially supported by the National Natural Science Foundation of China (10501045, 10771105), and the NCET and the Fund of the Personnel Division of Nankai University.

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

 DIAO Gao, LIU Xiu-Gui, JIN Ying-Long   

  1. School of Mathematical Sciences, Nankai University, Tianjin 300071, China
  • Received:2006-06-13 Revised:2007-03-05 Online:2009-03-20 Published:2009-03-20
  • Supported by:

    This research is partially supported by the National Natural Science Foundation of China (10501045, 10771105), and 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 nontrivial troduct of filtration, s + 6, in the stable homotopy groups of sphere, Πt−6S, which is represented up to non-zero scalar by βs+2h0(hmbn−1hnbm−1) ∈ Exts+6,t+sA (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 + pm + pn)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

Abstract:

By a method improving that of [1], the authors prove the existence of a nontrivial troduct of filtration, s + 6, in the stable homotopy groups of sphere, Πt−6S, which is represented up to non-zero scalar by βs+2h0(hmbn−1hnbm−1) ∈ Exts+6,t+sA (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 + pm + pn)q. The advantage of this method is to extend the range of s without much complicated argument as in [1].

Key words: Stable homotopy groups of spheres, Adams spectral sequence, May spectral sequence

中图分类号: 

  • 55Q45