Some Secondary Differentials on the Fourth Line of the Adams Spectral Sequence

Abstract

In this paper, we determine some nontrivial secondary Adams differentials on the fourth line \({\rm{Ext}}_{\cal A}^{4,*}(/p,/p)\) of the classical Adams spectral sequence. Specially, among these differentials, two of them are obtained via the matrix Massey products.

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Acknowledgements

The author will thank deeply the referee for his/her reading the original manuscript very carefully and giving many helpful suggestions, especially for his/her suggestions on future research related to this paper.

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Correspondence to Hao Zhao.

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Supported by NSFC (Grant Nos. 11671154, 11761072, 12001474 and 11871284) and Guangdong Natural Science Foundation (Grant No. 2020A1515011008) and “13th Five-Year” Science and Technology Project of Jilin Department of Education (Grant No. JJKH20200508KJ)

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Zhong, L.N., Hong, J.G. & Zhao, H. Some Secondary Differentials on the Fourth Line of the Adams Spectral Sequence. Acta. Math. Sin.-English Ser. (2021). https://doi.org/10.1007/s10114-021-0001-x

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Keywords

  • Stable homotopy groups of spheres
  • Adams spectral sequence
  • May spectral sequence
  • matrix Massey product

MR(2010) Subject Classification

  • 55Q45
  • 55T15
  • 55S10