#### Volume 9, issue 1 (2009)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
A Toda bracket in the stable homotopy groups of spheres

### Xiugui Liu

Algebraic & Geometric Topology 9 (2009) 221–236
##### Abstract

Let $p$ be a prime number greater than five. In the $p$–local stable homotopy groups of spheres, H Toda and J Lin, respectively, constructed the elements

$\begin{array}{cc}{\gamma }_{s}\in {\pi }_{2s{p}^{3}-2{p}^{2}-2p-2s+1}\left(S\right),& \\ {\omega }_{m,n}\in {\pi }_{2{p}^{n+1}-2{p}^{n}+2{p}^{m+1}-2{p}^{m}+2p-6}\left(S\right)& \end{array}$

of order $p$. In this paper, we show the nontriviality of the Toda bracket $〈{\gamma }_{s},p,{\omega }_{m,n}〉$ in the stable homotopy groups of spheres, where $n\ge m+2>6$, $3\le s.

##### Keywords
stable homotopy groups of sphere, Toda bracket, Adams spectral sequence, May spectral sequence
##### Mathematical Subject Classification 2000
Primary: 55Q45, 55T15
Secondary: 55S10
##### Publication
Revised: 10 December 2008
Accepted: 13 December 2008
Published: 3 February 2009
##### Authors
 Xiugui Liu School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 PR China