A Relation in the Stable Homotopy Groups of Spheres  

作　　者：Jianxia BAI Jianguo HONG 

机构地区：[1]Ren’ai College of Tianjin University [2]School of Mathematical Science, Nankai University

出　　处：《Chinese Annals of Mathematics,Series B》2015年第3期413-426,共14页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11071125,11261062,11471167);the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120031110025)

摘　　要：Let p ≥ 7 be an odd prime. Based on the Toda bracket 〈α1β1^p-1, α1β1,p, γs〉, the authors show that the relation α1β1^P-1h2,0γs= βp/p-1γ/s holds. As a resulL they can obtain α1β1^ph2,0γs= 0 ∈ π＊（S^0） for 2 ≤ s ≤ p - 2, even though α1h2,0γs and β1α1h2,0γs are not trivial. They also prove that β1^p-1 α1h2,0γ3 is nontrivial in π＊（S^0） and conjecture β1^p-1 α1h2,0γs is nontrivial in π＊（S^0） for 3 ≤s ≤ p - 2. Moreover, it is known that βp/p-1γ3 = 0 ∈ EXtBP＊Bp^5,＊（BP＊, BP＊）, but βp/p-1γ3 is nontrivial in π＊（S^0） and represents the element β1^p-1α1h2,0γ3.

关 键 词：Toda bracket Stable homotopy groups of spheres Adams-Novikovspectral sequence Method of infinite descent 

分 类 号：O152[理学—数学]