A ωn-Related Family of Homotopy Elements in the Stable Homotopy of Spheres

Citation:

Xiugui LIU,Jianming XIAO,Da ZHENG.A ωn-Related Family of Homotopy Elements in the Stable Homotopy of Spheres[J].Chinese Annals of Mathematics B,2018,39(5):849~860
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Authors:

Xiugui LIU; Jianming XIAO;Da ZHENG

Foundation:

This work was supported by the National Natural Science Foundation of China (No.11571186).
Abstract: To determine the stable homotopy groups of spheres $\pi_*(S)$ is one of the central problems in homotopy theory. Let $p$ be a prime greater than $5$. The authors make use of the May spectral sequence and the Adams spectral sequence to prove the existence of a $\varpi_n$-related family of homotopy elements, $\beta_1\omega_n\gamma_{s}$, in the stable homotopy groups of spheres, where $n>3$, $3\leq s

Keywords:

Stable homotopy groups of spheres, Adams spectral sequence, May spectral sequence

Classification:

55Q45
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