Detection of Some Elements in the Stable Homotopy Groups of Spheres

被引：0
作者：
Xiugui LIUDedicated to Professor Jinkun Lin on His th Birthday School of Mathematical Sciences and LPMCNankai UniversityTianjin China [65 ,300071 ]
机构：
来源：
Chinese Annals of Mathematics | 2008年 / 03期
关键词：
Stable homotopy groups of spheres; Adams spectral sequence; May spectral sequence; Steenrod algebra;
D O I：
暂无
中图分类号：
O189.23 [同伦论];
学科分类号：
070104 ;
摘要：
<正>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 spheresπ*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 spheresπp~nq+2pq+q-3S which is of order p and is represented by k_oh_n∈Ext3,P~nq+2pq+qA（Zp,Zp）in the Adams spectral sequence,where p≥5 is an odd prime,n≥3 and q=2（p-1）.In the course of the proof,a new family of homotopy elements inπp~nq+（p+1）q-1V（1）which is represented byβ*i'*i*（h_n）∈EXT2,p~nq+（p+1）q+1A(H*V（1）,Zp)in the Adams sequence is detected.
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页码：291 / 316
页数：26
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