A new family in the stable homotopy groups of spheres
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- by Xiugui Liu and Jianming Xiao
- Proc. Amer. Math. Soc. 151 (2023), 2241-2251
- DOI: https://doi.org/10.1090/proc/16286
- Published electronically: February 28, 2023
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Abstract:
In this paper, the nontriviality of homotopy elements $\beta _1\varrho _s$ in the $p$-primary component of stable homotopy groups of spheres is shown by virtue of the Adams spectral sequence and the May spectral sequence, where $\varrho _s$ is represented by $b_0g_{0}\widetilde {\gamma }_{s}$ in the Adams spectral sequence, $p$ is a prime number greater than $5$, and $3\leq s<p$.References
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Bibliographic Information
- Xiugui Liu
- Affiliation: School of Mathematical Sciences and LPMC, Nankai University, No. 94 Weijin Road, Nankai District, 300071 Tianjin, Peopleโs Republic of China
- Email: matlxg@126.com
- Jianming Xiao
- Affiliation: School of Mathematics, Renmin University of China, No. 59 Zhongguancun Street, Haidian District Beijing, 100872 Beijing, Peopleโs Republic of China
- Email: xiaojianming@ruc.edu.cn
- Received by editor(s): June 6, 2022
- Received by editor(s) in revised form: August 15, 2022, August 17, 2022, and August 18, 2022
- Published electronically: February 28, 2023
- Additional Notes: The first author was supported in part by the National Natural Science Foundation of China (Grant No. 12171165) and Tianjin Natural Science Foundation (Grant No. 19JCYBJC30200). Both authors contributed equally to this paper and are listed in alphabetical order.
- Communicated by: Julie Bergner
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 2241-2251
- MSC (2020): Primary 55Q45, 55T10
- DOI: https://doi.org/10.1090/proc/16286
- MathSciNet review: 4556214