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Chinese Annals of Mathematics, Series B

, Volume 39, Issue 5, pp 849–860 | Cite as

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

  • Xiugui Liu
  • Jianming Xiao
  • Da Zheng
Article

Abstract

To determine the stable homotopy groups of spheres π*(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 ϖn-related family of homotopy elements, β1ωnγs, in the stable homotopy groups of spheres, where n > 3, 3 ≤ s < p − 2 and the ϖn-element was detected by X. Liu.

Keywords

Stable homotopy groups of spheres Adams spectral sequence May spectral sequence 

2000 MR Subject Classification

55Q45 

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Notes

Acknowledgement

The authors would like to express their deep thanks to the referee. He read carefully the manuscript of this paper and gave the authors many helpful comments and suggestions.

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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical Sciences and LPMCNankai UniversityTianjinChina
  2. 2.School of InformationRenmin University of ChinaBeijingChina
  3. 3.School of Mathematical SciencesNankai UniversityTianjinChina

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