数学物理学报(英文版)

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A NEW FAMILY OF FILTRATION S+5 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

王玉玉   

  1. 天津师范大学数学学院, 天津 300387
  • 收稿日期:2005-12-19 修回日期:1900-01-01 出版日期:2008-04-20 发布日期:2008-04-20
  • 通讯作者: 王玉玉
  • 基金资助:

    Supported by NFSC (10171049)

A NEW FAMILY OF FILTRATION S+5 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

Wang Yuyu   

  1. School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China
  • Received:2005-12-19 Revised:1900-01-01 Online:2008-04-20 Published:2008-04-20
  • Contact: Wang Yuyu

摘要:

In this article, by the algebraic method, the author proves the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres $\pi_rS$, which is represented by 0 ≠\widetilde{\gamma}_{s+3}h_nh_m\in {\rm Ex}t_A^{s+5,\ t}(Z_p, Z_p)$ in the Adams spectral sequence, where r=q(pm+pn+(s+3)p2+(s+2)p+(s+1))-5}, t=pmq+pnq+(s+3)p2q+(s+2)pq+(s+1)q+s, p≥7, m≥n+2>5, 0≤s

关键词: Stable homotopy of spheres, Adams spectral sequence, cofiberation,
May spectral sequence

Abstract:

In this article, by the algebraic method, the author proves the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres $\pi_rS$, which is represented by 0 ≠\widetilde{\gamma}_{s+3}h_nh_m\in {\rm Ex}t_A^{s+5,\ t}(Z_p, Z_p)$ in the Adams spectral sequence, where r=q(pm+pn+(s+3)p2+(s+2)p+(s+1))-5}, t=pmq+pnq+(s+3)p2q+(s+2)pq+(s+1)q+s, p≥7, m≥n+2>5, 0≤s

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

中图分类号: 

  • 55Q45