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
This paper constructs a new family in the stable homotopy of spheres π_(t-)S represented by h_ngoY_3 ∈E_2~6(,t) in the Adams spctral sequence which revisits the b_(n-1goY3)-elements ∈π_(-7)S con- structced in[3]. ...This paper constructs a new family in the stable homotopy of spheres π_(t-)S represented by h_ngoY_3 ∈E_2~6(,t) in the Adams spctral sequence which revisits the b_(n-1goY3)-elements ∈π_(-7)S con- structced in[3]. where t=2p^(11)(p-1)+6(p^2+p+1)(p-1)and p≥7 is a prime. 11≥4展开更多
In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres ;π-6S which is represented by hngoγ^-3 ∈ Ext^6tA（Zp, Zp） in the Adams spectral sequence, where t = 2p^n（p- 1）＋ 6（p^2...In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres ;π-6S which is represented by hngoγ^-3 ∈ Ext^6tA（Zp, Zp） in the Adams spectral sequence, where t = 2p^n（p- 1）＋ 6（p^2 ＋p ＋ 1）（p- 1） and p ≥ 7 is a prime number. This article generalizes the result and proves the existence of a new nontrivial family of filtration s ＋ 6 in the stable homotopy groups of spheres πt1-8-6S which is represented by bygoγ^s＋3 ∈ Ext^s＋6＋t1Atl （Zp, Zp） in the Adams spectral sequence, where n≥ 4, 0 ≤ s 〈 p - 4, t1 = 2p^n（p- 1） ＋ 2（p- 1）（（s ＋ 3）p^2 ＋ （s ＋ 3）p ＋ （s ＋ 3）） ＋ s.展开更多
In this paper, it is proved that for p≥7 an arbitrary odd prime and 3≤s 〈 p, the homotopy elements β1λs and α1λs are nontrivial in the stable homotopy groups of spheres π＊S.
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).
基金Supported by National Natural Science Foundation. Project 10171049.
文摘This paper constructs a new family in the stable homotopy of spheres π_(t-)S represented by h_ngoY_3 ∈E_2~6(,t) in the Adams spctral sequence which revisits the b_(n-1goY3)-elements ∈π_(-7)S con- structced in[3]. where t=2p^(11)(p-1)+6(p^2+p+1)(p-1)and p≥7 is a prime. 11≥4
基金Supported by the National Natural Science Foundation of China (1051045)the Youth Project of Tianyuan Foundation of China (10426028)the China Postdoctoral,Science Foundation and Fund of the Personnel Division of Nankai University
文摘In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres ;π-6S which is represented by hngoγ^-3 ∈ Ext^6tA（Zp, Zp） in the Adams spectral sequence, where t = 2p^n（p- 1）＋ 6（p^2 ＋p ＋ 1）（p- 1） and p ≥ 7 is a prime number. This article generalizes the result and proves the existence of a new nontrivial family of filtration s ＋ 6 in the stable homotopy groups of spheres πt1-8-6S which is represented by bygoγ^s＋3 ∈ Ext^s＋6＋t1Atl （Zp, Zp） in the Adams spectral sequence, where n≥ 4, 0 ≤ s 〈 p - 4, t1 = 2p^n（p- 1） ＋ 2（p- 1）（（s ＋ 3）p^2 ＋ （s ＋ 3）p ＋ （s ＋ 3）） ＋ s.
文摘In this paper, it is proved that for p≥7 an arbitrary odd prime and 3≤s 〈 p, the homotopy elements β1λs and α1λs are nontrivial in the stable homotopy groups of spheres π＊S.
基金This work is supported by the NSFC(No. 10171049)the Youth Project of Tianyuan Foundation of China(No.10426028)+1 种基金the China Postdoctoral Science Foundation(No. 2004036301)the Fund of the Personnel Division of Nankai University(No. J02017)
基金Supported by the National Natural Science Foundation of China ( No .10501045) ,the Fund of the personnel Division of Nankai University , the Youth Project ofTianyuan Foundation of China( No .10426028) and the China Postdoctoral ScienceFoundation
基金Supported by the National Natural Science Foundation of China(1130138611026197+2 种基金11226080)the Outstanding Youth Teacher Foundation of Tianjin(ZX110QN044)the Doctor Foundation of Tianjin Normal University(52XB1011)
基金Supported by NSFC(11301386)NSFC(11001195)+1 种基金Beiyang Elite Scholar Program of Tianjin University(0903061016)The Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
