The composition of R.~Cohen's elements and the third periodic elements in stable homotopy groups of spheres

Xing Gu; Xiangjun Wang; Jianqiu Wu

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arXiv · 1903.02730

The composition of R.~Cohen's elements and the third periodic elements in stable homotopy groups of spheres

Xing Gu·Xiangjun Wang·Jianqiu Wu

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Abstract

In this paper, we study the cohomology of the Morava stabilizer algebra $S(3)$. As an application, we show that for $p \geq 7$, if $s\not \equiv 0, \pm 1 \,\, mod \,p $, $n\not \equiv 1 \,\, mod\, 3$, $n>1$, then $\zeta_n\gamma_s$ is a nontrivial product in $\pi_*(S)$ by Adams-Novikov spectral sequence, where $\zeta_n$ is created by R. Cohen \cite{Co}, $\gamma_s$ is a third periodic homotopy elements.

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Xing Gu, Xiangjun Wang, Jianqiu Wu. 2019-03-07. The composition of R.~Cohen's elements and the third periodic elements in stable homotopy groups of spheres. https://arxiv.org/abs/1903.02730

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