A nontrivial product in the stable homotopy groups of spheres  

作　　者：LIU XiuguiInstitute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China 

出　　处：《Science China Mathematics》2004年第6期831-841,共11页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.10171049);the Youth Project of Tianyuan Foundation(Grant No.10426028).

摘　　要：Let A be the mod p Steenrod algebra for p an arbitrary odd prime. In 1962, Liulevicius described h i and b k in Ext* A ’*(Zp,Zp) having bigrading (1, sui— 1) and (2, 2p k+1 x(p— 1)), respectively. In this paper we prove that for p ≥ 7, n ≥ 4 and $3 \leqslant s < p - 1, h_0 b_{n - 1} \tilde \gamma _s \in Ext_A^{s + 3,p^n q + sp^2 q + (s - 1)pq + (s - 1)q + s - 3} (Z_p ,Z_p )$ survives to E∞ in the Adams spectral sequence, where q = 2(p — 1).

关 键 词：stable homotopy groups of spheres Adams spectral sequence Toda-Smith spectra May spectral sequence 

分 类 号：O189.23[理学—数学]