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: 104        Net amount: 223

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

Organizer:The Ministry of Education of China Sponsor:Fudan University Address:220 Handan Road, Fudan University, Shanghai, China E-mail:edcam@fudan.edu.cn
Designed by Beijing E-Tiller Co.,Ltd.