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| A Nontrivial Homotopy Element of Order p2 Detected by the Classical Adams Spectral Sequence |
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Citation： |
Hao ZHAO,Linan ZHONG.A Nontrivial Homotopy Element of Order p2 Detected by the Classical Adams Spectral Sequence[J].Chinese Annals of Mathematics B,2018,39(1):1~8 |
| Page view： 1664
Net amount： 1249 |
Authors： |
Hao ZHAO; Linan ZHONG |
Foundation： |
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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| Abstract： |
Let $p$ be an odd prime. The authors detect a nontrivial element
$\widetilde{a}_p$ of order $p^2$ in the stable homotopy groups of
spheres by the classical Adams spectral sequence. It is represented
by $a_{0}^{p-2}h_{1}\in{\rm Ext}_A^{p-1,pq+p-2}(\mathbb{Z}/p,
\mathbb{Z}/p)$ in the $E_2$-term of the ASS and meanwhile $p\cdot
\widetilde{a}_p$ is the first periodic element $\alpha_p$. |
Keywords： |
Stable homotopy groups of sphere, Adams spectral sequence, May spectral sequence, Massey product |
Classification： |
55Q45 |
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