
 
A Nontrivial Homotopy Element of Order p^{2} Detected by the Classical Adams Spectral Sequence 
 
Citation： 
Hao ZHAO,Linan ZHONG.A Nontrivial Homotopy Element of Order p^{2} Detected by the Classical Adams Spectral Sequence[J].Chinese Annals of Mathematics B,2018,39(1):1~8 
Page view： 738
Net amount： 645 
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). 


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 $a_{0}^{p2}h_{1}\in{\rm Ext}_A^{p1,pq+p2}(\mathbb{Z}/p,
\mathbb{Z}/p)$ 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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