A Nontrivial Homotopy Element of Order p2 Detected by the Classical Adams Spectral Sequence 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： 288        Net amount： 343 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 $a_{0}^{p-2}h_{1}\in{\rm Ext}_A^{p-1,pq+p-2}(\mathbb{Z}/p, \mathbb{Z}/p)$ 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 Download PDF Full-Text