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 共查询到17条相似文献,搜索用时 109 毫秒
1.
利用Adams谱序列与May谱序列, 发掘了球面稳定同伦群中一族$\xi_n$的相关元素. 这里$\xi_n\in\pi_* M$在Adams 谱序列中由$h_0h_n\in \ext_A^{2,p^n q+q}(H^* M,\zz_p)$所表示, 其中$p\geqslant 7,\ n>3,\ q=2(p-1).$  相似文献   

2.
证明了古典Adams谱序列中的乘积元b_0~2β_s∈Ext_A~(s+4,t(s))(Z_p,Z_p)的非平凡性,其中p≥11,2≤sp-2,t(s)=2(p-1)[(s+2)p+(s-1)]+(s-2).  相似文献   

3.
证明了模p-Steenrod代数高维上同调群中的乘积元b_0~2γs∈Ext_A~(s+4,t(s))(Z_p,Z_p)的非平凡性,其中p≥11,3≤sp-1,t(s)=2(p-1)[sp~2+(s+1)p+(s-2)]+(s-3).  相似文献   

4.
设 $p\geq 7$ 为任意奇素数. 证明了当 $3\leq s 相似文献   

5.
主要用May谱序列证明了非平凡的乘积b_0k_0δ_(s+4)∈Ext_A~(s+8,t)(Z_p,Z_p),其中p是大于等于7的素数,0≤sp-4,q=2(p-1),t=(s+4)p~3q+(s+3)p~2q+(s+5)pq+(s+2)q+s.  相似文献   

6.
球面稳定同伦群中的一个非平凡积   总被引:1,自引:0,他引:1       下载免费PDF全文
刘秀贵 《中国科学A辑》2004,34(4):429-439
p≥7为任意奇素数, A为模p的Steenrod代数. 1962年, A. Liulevicius在他的文章中指出元素hi, bk∈Ext*A(Zp, Zp)分别具有双次数(1, 2pi(p&#8722;1))和(2, 2pk+1(p&#8722;1)). 我们证明: 当p≥7, n≥4, 3≤s<p&#8722;1时, 积h0hn-1rs ∈ ExtAs+3,p+sp2q+(s-1)pq+(s-1)q+s-3(Zp,Zp)收敛到Z, 其中q=2(p&#8722;1).  相似文献   

7.
刘秀贵  赵永强 《数学杂志》2006,26(4):393-398
本文研究了球面稳定同伦中同伦元素β2γs的非平凡性.利用May谱序列和Adams谱序列证明:同伦元素β2γs在一定条件下是阶为p的非平凡元素,其中p≥7是奇素数.  相似文献   

8.
决定球面稳定同伦群是同伦论中的核心问题之一,是非常重要的.该文证明:球面稳定同伦元素α1β1βs是一个阶为p的非平凡元素,其中p≥5是任意奇素数,1≤s相似文献   

9.
王玉玉  王健波 《数学杂志》2017,37(5):898-910
本文研究了球面稳定同伦群的问题.以Adams谱序列中的第二非平凡微分为几何输入,给出了球面稳定同伦群中h0gnn > 3)的收敛性.同时,由Yoneda乘积的知识,发掘了球面稳定同伦群中的一个非平凡新元素.非平凡元素的范围将被我们的结果进一步扩大.  相似文献   

10.
刘秀贵 《数学进展》2006,35(6):733-738
本文证明:当p≥7任意奇素数,3≤s相似文献   

11.
In this paper, the authors introduce a new effective method to compute the generators of the E1-term of the May spectral sequence. This helps them to obtain four families of non-trivial product elements in the stable homotopy groups of spheres.  相似文献   

12.
Let A be the mod p Steenrod algebra and S be the sphere spectrum localized at an odd prime p. To determine the stable homotopy groups of spheres π*S is one of the central problems in homotopy theory. This paper constructs a new nontrivial family of homotopy elements in the stable homotopy groups of spheres πp^nq+2pq+q-3S which isof order p and is represented by kohn ∈ ExtA^3,P^nq+2pq+q(Zp,Zp) in the Adams spectral sequence, wherep 〉 5 is an odd prime, n ≥3 and q = 2(p-1). In the course of the proof, a new family of homotopy elements in πp^nq+(p+1)q-1V(1) which is represented by β*i'*i*(hn) ∈ ExtA^2,pnq+(p+1)q+1 (H^*V(1), Zp) in the Adams sequence is detected.  相似文献   

13.
Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by (b0hn-h1bn-1)∈ ExtA^3,(p^n+p)q(Zp,Zp) in the Adams spectral sequence. At the same time, he proved that i.(hlhn) ∈ExtA^2,(p^n+P)q(H^*M, Zp) is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π(p^n+p)q-2M. In this paper, with Lin's results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq + sp^2q + spq + (s - 2)q + s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s+2,*-term of the Adams spectral sequence, where p ≥ 7, q = 2(p - 1), n ≥ 4 and 3 ≤ s 〈 p.  相似文献   

14.
This paper proves the existence of an order p element in the stable homotopy group of sphere spectrum of degree pnq pmq q - 4 and a nontrivial element in the stable homotopy group of Moore spectum of degree pnq pmq q - 3 which are represented by h0(hmbn-1-hnbm-1) and i*(h0hnhm) in the E2-terms of the Adams spectral sequence respectively, where p≥7 is a prime, n≥m 2≥4, q = 2(p - 1).  相似文献   

15.
In this paper, some groups Ext A^s.t (Zp, Zp) with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πpnq+(s+3)pq+(s+1)q-5S which is represented (up to a nonzero scalar) by β+2bohh∈ExtA^s+5,P^nq+(n+3)pq+(n+1)q+s(Zp, Zp) in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2(p - 1).  相似文献   

16.
设$p\geq 7$素数,$A$为模$p$的Steenrod代数. 我们利用Adams谱序列证明了球面稳定同伦群$\pi_{\ast}S$中,存在由$b_1g_0\tilde{\gamma}_{s}\in Ext_A^{s+4,(s+1)p^2q+spq+sq+s-3}(Z_p,Z_p)$所表示的新的非平凡元素族,其中$q=2(p-1)$, $3\leq s相似文献   

17.
In this article, by the algebraic method, the author proves the existence of a new nontrivial family of filtration s + 5 in the stable homotopy groups of spheres πrS,which is represented by 0 ≠γ^-s+3hnhm∈Ext^s+5,A ^t(Zp,Zp)in the Adams spectral sequence,where r=q(p^m+p^n+(s+3)p^2+(s+2)p+(s+1))-5,t=p^mq+p^nq+(s+3)p^2q+(s+2)pq+(s+1)q+s,p≥7,m≥n+2〉5,0≤s〈p-3,q=2(p-1).  相似文献   

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