A Relation in the Stable Homotopy Groups of Spheres

被引：0

作者：

Jianxia BAI ^{[1
]}

Jianguo HONG ^{[2
]}

机构：

[1] Ren’ai College of Tianjin University

[2] School of Mathematical Science, Nankai University

来源：

Chinese Annals of Mathematics(Series B) | 2015年 / 36卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Toda bracket; Stable homotopy groups of spheres; Adams-Novikov spectral sequence; Method of infinite descent;

D O I：

暂无

中图分类号：

O152 [群论];

学科分类号：

070104 ;

摘要：

Let p≥7 be an odd prime. Based on the Toda bracket α1βp-11, α1 β1, p, γs,the authors show that the relation α1βp-11h2,0 γs= βp/p-1γs holds. As a result, they can obtain α1βp1h2,0 γs = 0 ∈π*(S0) for 2≤s≤p- 2, even though α1h2,0γs and β1α1h2,0 γs are not trivial. They also prove that βp-11α1 h2,0 γ3 is nontrivial in π*(S0) and conjecture that βp-11α1 h2,0 γs is nontrivial in π*(S0) for 3≤s≤p- 2. Moreover, it is known thatβp/p-1γ3 = 0 ∈ Ext5,*BP*BP(BP*, BP*), but βp/p-1γ3 is nontrivial in π*(S0) and represents the element βp-11α1 h2,0 γ3.

引用

页码：413 / 426

页数：14

共 44 条

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