Algebraic & Geometric Topology

A Toda bracket in the stable homotopy groups of spheres

Xiugui Liu

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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

γ s π 2 s p 3 2 p 2 2 p 2 s + 1 ( S ) , ω m , n π 2 p n + 1 2 p n + 2 p m + 1 2 p m + 2 p 6 ( 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 nm+2>6, 3s<p.

Article information

Source
Algebr. Geom. Topol., Volume 9, Number 1 (2009), 221-236.

Dates
Received: 24 May 2007
Revised: 10 December 2008
Accepted: 13 December 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796962

Digital Object Identifier
doi:10.2140/agt.2009.9.221

Mathematical Reviews number (MathSciNet)
MR2482074

Zentralblatt MATH identifier
1168.55013

Subjects
Primary: 55Q45: Stable homotopy of spheres 55T15: Adams spectral sequences
Secondary: 55S10: Steenrod algebra

Keywords
stable homotopy groups of sphere Toda bracket Adams spectral sequence May spectral sequence

Citation

Liu, Xiugui. A Toda bracket in the stable homotopy groups of spheres. Algebr. Geom. Topol. 9 (2009), no. 1, 221--236. doi:10.2140/agt.2009.9.221. https://projecteuclid.org/euclid.agt/1513796962


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