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

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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.

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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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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tian**, 300071, China

    **ugui Liu

  2. School of Information, Renmin University of China, Bei**g, 100872, China

    Jianming **ao

  3. School of Mathematical Sciences, Nankai University, Tian**, 300071, China

    Da Zheng

Authors
  1. **ugui Liu
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  2. Jianming **ao
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  3. Da Zheng
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Corresponding author

Correspondence to Jianming **ao.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11571186).

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Liu, X., **ao, J. & Zheng, D. A ϖn-Related Family of Homotopy Elements in the Stable Homotopy of Spheres. Chin. Ann. Math. Ser. B 39, 849–860 (2018). https://doi.org/10.1007/s11401-018-0100-x

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  • DOI: https://doi.org/10.1007/s11401-018-0100-x

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