## Algebraic & Geometric Topology

### A Toda bracket in the stable homotopy groups of spheres

Xiugui Liu

#### 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 $n≥m+2>6$, $3≤s.

#### Article information

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

Dates
Revised: 10 December 2008
Accepted: 13 December 2008
First available in Project Euclid: 20 December 2017

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

#### 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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