On Nontriviality of a Product in the Classical Adams Spectral Sequence

Authors

  • Linan Zhong Department of Mathematics, Yanbian University, Yanji, 133002, China
  • Hao Zhao School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

DOI:

https://doi.org/10.37256/cm.4420232994

Keywords:

stable homotopy groups of sphere, Adams spectral sequences, May spectral sequences

Abstract

Let p ≥ 11 be an odd prime and q = 2(p − 1). Suppose that n ≥ 1 with n ≠ 5. Let 0 ≤ s < p − 4 and t = s + 2 + t = s + 2 + (s + 2)p + (s + 3)p2 + (s +4)p3 + pn . This paper shows that the product element δs+4h0bn−1 ∈ ExtAs+7,tq+s (Z/p,Z/p) is a nontrivial permanent cycle in the classical Adams spectral sequence, where δs+4 denotes the 4th Greek letter element.

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Published

2023-11-17

Issue

Contemporary Mathematics, Volume 4 Issue 4 (2023), 620-1346

Section

Research Article

License

Copyright (c) 2023 Hao Zhao, et al.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

1.
On Nontriviality of a Product in the Classical Adams Spectral Sequence. Contemp. Math. [Internet]. 2023 Nov. 17 [cited 2025 Dec. 24];4(4):995-1013. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/2994