Volume 9, issue 1 (2009)

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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

γs π2sp32p22p2s+1(S), ωm,n π2pn+12pn+2pm+12pm+2p6(S)

of order p. In this paper, we show the nontriviality of the Toda bracket γs,p,ωm,n in the stable homotopy groups of spheres, where n m + 2 > 6, 3 s < p.

Keywords
stable homotopy groups of sphere, Toda bracket, Adams spectral sequence, May spectral sequence
Mathematical Subject Classification 2000
Primary: 55Q45, 55T15
Secondary: 55S10
References
Publication
Received: 24 May 2007
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