Abstract
Let p be an odd prime. The authors detect a nontrivial element ã p of order p2 in the stable homotopy groups of spheres by the classical Adams spectral sequence. It is represented by \(a_0^{p - 2} h_1 \in Ext_A^{p - 1,pq + p - 2} (\mathbb{Z}/p,\mathbb{Z}/p)\) in the E2-term of the ASS and meanwhile p · ãp is the first periodic element αp.
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Acknowledgments
The authors would like to give their thanks to the referee for his/her many helpful suggestions on the original version of this paper, and they also acknowledge the financial support of the Institute for Mathematical Science during their stay at the National University of Singapore in August 2015.
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This work was supported by the National Natural Science Foundation of China (Nos. 11761072, 11671154) and the China Postdoctoral Science Foundation Special Funded Project (No. 2015T80909).
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Zhao, H., Zhong, L. A nontrivial homotopy element of order p2 detected by the classical Adams spectral sequence. Chin. Ann. Math. Ser. B 39, 1–8 (2018). https://doi.org/10.1007/s11401-018-1046-8
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DOI: https://doi.org/10.1007/s11401-018-1046-8