This paper proves the existence of an order p element in the stable homotopy group of sphere spectrum of degree p^nq ＋p^mq ＋ q- 4 and a nontrivial element in the stable homotopy group of Moore spectum of degree p^nq...This paper proves the existence of an order p element in the stable homotopy group of sphere spectrum of degree p^nq ＋p^mq ＋ q- 4 and a nontrivial element in the stable homotopy group of Moore spectum of degree p^nq ＋ p^mq ＋ q - 3 which are represented by h0（hmbn-1 - hnbm-1） and ie（hohnhm） in the E2-terms of the Adams spectral sequence respectively, where p ≥ 7 is a prime, n ≥ m ＋ 2 ≥ 4, q = 2（p - 1）.展开更多
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 ...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).展开更多
基金Project supported by the National Natural Science Foundation of China (No.10171049)
文摘This paper proves the existence of an order p element in the stable homotopy group of sphere spectrum of degree p^nq ＋p^mq ＋ q- 4 and a nontrivial element in the stable homotopy group of Moore spectum of degree p^nq ＋ p^mq ＋ q - 3 which are represented by h0（hmbn-1 - hnbm-1） and ie（hohnhm） in the E2-terms of the Adams spectral sequence respectively, where p ≥ 7 is a prime, n ≥ m ＋ 2 ≥ 4, q = 2（p - 1）.
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).
文摘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).
