Detection of Some Elements in the Stable Homotopy Groups of Spheres

作     者：Xiugui LIU 

作者机构：School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2008年第29卷第3期

页      面：291-316页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：the National Natural Science Foundation of China(Nos.10501045,10771105) the Fund of the Personnel Division of Nankai University(No.J02017) 

主　　题：Stable homotopy groups of spheres Adams spectral sequence Mayspectral sequence Steenrod algebra 

摘      要：Let A be the mod p Steenrod algebra and S be the sphere spectrum localized at an odd prime p. To determine the stable homotopy groups of spheres π＊S is one of the central problems in homotopy theory. This paper constructs a new nontrivial family of homotopy elements in the stable homotopy groups of spheres πp^nq＋2pq＋q-3S which isof order p and is represented by kohn ∈ ExtA^3,P^nq＋2pq＋q（Zp,Zp） in the Adams spectral sequence, wherep 〉 5 is an odd prime, n ≥3 and q = 2（p-1）. In the course of the proof, a new family of homotopy elements in πp^nq＋（p＋1）q-1V（1） which is represented by β＊i＇＊i＊（hn） ∈ ExtA^2,pnq＋（p＋1）q＋1 （H^＊V（1）, Zp） in the Adams sequence is detected.