球面稳定同伦群的两个新元素h0(b1)3γ3 和(b1)3g0γ3

球面稳定同伦群的两个新元素h₀(b₁)³γ₃ 和(b₁)³g₀γ₃

肖建明^1,2, 黄宇慧²

1. 南开大学数学系，天津 300071; 2. 吉林商业高等专科学校基础部，长春 130031

收稿日期:2002-11-27 修回日期:1900-01-01 出版日期:2003-07-26 发布日期:2003-07-26
通讯作者: 肖建明

Two New Elements of the Stable Homotopy Group of Spheres h>sub>0(b₁)³γ₃ and (b_{1,/sub>)³g₀γ,sub>3}

XIAO Jian-ming^1,2, HUANG Yu-hui²

1. Department of Mathematics, Nankai University, Tianjin 300071, China; 2. Department of Foundation, Jilin Commercial College, Changchun 130031, China

Received:2002-11-27 Revised:1900-01-01 Online:2003-07-26 Published:2003-07-26
Contact: XIAO Jian-ming

摘要/Abstract

摘要： 证明了在p≥11时, 0≠h₀(b₁)³∈Ext^{7, 3p²q+q}_A(H^*V(2),Z_p)和0≠(b₁)³h₀∈Ext^{8,3p²q+pq+2q}_{A(H^*V(2),Z_p)在Adams谱序列中分别收敛到π_*V(2) 的非零元， 0≠h₀(b₁)³γ₃Ext^{10 ,6p²q+2pq+2q}_Ap,Z_p)和0≠(b1})³g₀γ₃∈Ext^{11,6p²q+3p q+3q}_A(Z_p,Z_p)在Adams谱序列中分别收敛到π*S的非零元.

关键词: May谱序列, Adams谱序列, V(2)的Ext群, 球面稳定同伦群

Abstract: This paper proves that p≥11, 0≠h₀(b₁)³∈Ext^7,3p²q+q_A(H^*V(2),Z_{p) and 0≠(b₁)³g₀∈Ext^{8,3p²q+p q+2q}_A(H^*V(2),Z_p) in Adams spectral seqenc es converge to the nonzero elements of π_*V(2) of p order respectivel y while 0≠h₀(b₁)³γ₃∈Ext^{10,6p ²q+2pq+2q}_A(Z_p,Z_p) and 0≠(b1})³g₀γ₃∈Ext^{11,6p²q+3p q+3q}_A(Z_p,Z_p) in Adams spectral sequences converge to the nonzero elements of π_*S of p order respectively.

Key words: May spectral sequence, Adams spectral sequence, Extgroup of V(2), stable homotopy group of sphere

中图分类号:

O189.23

肖建明, 黄宇慧. 球面稳定同伦群的两个新元素h₀(b₁)³γ₃ 和(b₁)³g₀γ₃[J]. J4, 2003, 41(03): 294-298.

XIAO Jian-ming, HUANG Yu-hui. Two New Elements of the Stable Homotopy Group of Spheres h>sub>0(b₁)³γ₃ and (b_{1,/sub>)³g₀γ,sub>3}[J]. J4, 2003, 41(03): 294-298.

球面稳定同伦群的两个新元素h₀(b₁)³γ₃ 和(b₁)³g₀γ₃

Two New Elements of the Stable Homotopy Group of Spheres h>sub>0(b₁)³γ₃ and (b_{1,/sub>)³g₀γ,sub>3}

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