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共有20条相似文献,以下是第1-20项 搜索用时 187 毫秒

1.  A Nontrivial Product of Filtration s + 5 in the Stable Homotopy of Spheres  
   Xiu Gui LIU《数学学报(英文版)》,2007年第23卷第3期
   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).    

2.  Detection of Some Elements in the Stable Homotopy Groups of Spheres  
   Xiugui LIU《数学年刊B辑(英文版)》,2008年第29卷第3期
   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.    

3.  SOME NEW FAMILIES OF FILTRATION FIVE IN THE STABLE HOMOTOPY OF SPHERES  
   林金坤《数学物理学报(B辑英文版)》,2009年第29卷第5期
   This study proves a general result on convergence of α2x ∈ ExtA^s+2.tq+2q+1 (Zp, Zp) in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres πtq+2q-4S which is represented in the Adams spectral sequence by α2fn,α2fn,α2huhmhn ∈ ExtA^5,tq+2q+1(Zp,Zp) with tq=p^n+1q+2p^nq,2p^n+1q_P^nq,p^uq+p^mq+p^nq,respectively, where α2∈Extα^2,2q+1(Zp,Zp),fn∈ExtA^3,p^n+1q+2p^nq(Zp,Zp),fn∈ExtA^3,2p^n+2q+p^nq(Zp,Zp),hn∈ExtA^1,p^nq(Zp,Zp)and p≥5 is a prime,q=2(p=-1),n≥2.    

4.  A NEW FAMILY OF FILTRATION s+6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES  
   刘秀贵《数学物理学报(B辑英文版)》,2006年第26卷第2期
   In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres πt-6S which is represented by hngor3 ∈ ExtA6,t(Zp,Zp) in the Adams spectral sequence, where t=2pn(p-1) 6(p2 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-s-6S which is represented by hngors 3 6 ExtAs 6,t1(Zp, Zp) in the Adams spectral sequence, where n≥4, 0≤s    

5.  ON AN INFINITE FAMILY IN π*S  
   刘秀贵《数学物理学报(B辑英文版)》,2014年第1期
   In this paper, a new family of homotopy elements in the stable homotopy groups of spheres represented by h1hnhm γ?s in the Adams spectral sequence is detected, where n-2≥m≥5 and 3≤s 〈p.    

6.  On the Convergence of Products γ^-sh1hn in the Adams Spectral Sequence  
   Xiu Gui LIU《数学学报(英文版)》,2007年第23卷第6期
   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.    

7.  A NON-TRIVIAL PRODUCT OF FILTRATION s+6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES  
   赵浩  刘秀贵  金应龙《数学物理学报(B辑英文版)》,2009年第29卷第2期
   By a method improving that of [1], the authors prove the existence of a non-trivial product of filtration, s + 6, in the stable homotopy groups of sphere, πt-6S, which is represented up to non-zero scalar by β^-s+2ho(hmbn-1 -hnbm-1) ∈ ExtA^s+6,t+s(Zp, Zp) in the Adams spectral sequence, where p ≥ 7, n ≥ m + 2 ≥ 5, q = 2(p- 1), 0 ≤ s 〈 p - 2, t= (s + 2 + (s + 2)p + p^m + p^n)q. The advantage of this method is to extend the range of s without much complicated argument as in [1].    

8.  A pull back theorem in the Adams spectral sequence  
   Jin Kun Lin《数学学报(英文版)》,2008年第24卷第3期
   This paper proves that, for any generator x∈ExtA^s,tq(Zp,Zp), if (1L ∧i)*Ф*(x)∈ExtA^s+1,tq+2q(H*L∧M, Zp) is a permanent cycle in the Adams spectral sequence (ASS), then b0x ∈ExtA^s+1,tq+q(Zp, Zp) also is a permenent cycle in the ASS. As an application, the paper obtains that h0hnhm∈ExtA^3,pnq+p^mq+q(Zp, Zp) is a permanent cycle in the ASS and it converges to elements of order p in the stable homotopy groups of spheres πp^nq+p^mq+q-3S, where p ≥5 is a prime, s ≤ 4, n ≥m+2≥4 and M is the Moore spectrum.    

9.  《数学学报》英文版Vol.23(2007),No.3论文摘要  
   《数学学报》,2007年第50卷第3期
   A Nontrivial Produet ofFiltrations 5 inthestableHomotoPyofSPheres Xiu Gui LIU Abstraet In this paper,some盯oups Ext文‘(易,吞)with speeialized吕and t are first eomPuted勿the May sPeetral sequenee.Then we make use of the Adams sPeetral sequenee to prove the existenee of a new nontrivial family of filtrations 5 in the stable homotoPy groups of spheres7rP件。 (, 3),。 (s l)。一55 whieh 15 represented(up to a nonzero sealar)勿口: 2。。h。。Ext犷5,p”q (’ 3)pq (‘ ‘)“ “(几,吞)in t…    

10.  A ■_n-Related Family of Homotopy Elements in the Stable Homotopy of Spheres  
   Xiugui LIU  Jianming XIAO  Da ZHENG《数学年刊B辑(英文版)》,2018年第5期
   To determine the stable homotopy groups of spheres π_*(S) is one of the central problems in homotopy theory. Let p be a prime greater than 5. The authors make use of the May spectral sequence and the Adams spectral sequence to prove the existence of a ■_n-related family of homotopy elements, β1ω_nγ_s, in the stable homotopy groups of spheres, where ■_n 3, 3≤s p-2 and the ■_n-element was detected by X. Liu.    

11.  Two New Families in the Stable Homotopy Groups of Sphere and Moore Spectrum  
   Jinkun LIN《数学年刊B辑(英文版)》,2006年第27卷第3期
   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).    

12.  A Nontrivial Homotopy Element of Order p~2 Detected by the Classical Adams Spectral Sequence  
   Hao ZHAO  Linan ZHONG《数学年刊B辑(英文版)》,2018年第1期
   Let p be an odd prime.The authors detect a nontrivial element 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 ∈ Ext_A~(p-1,pq+p-2)(Z/p,Z/p) in the E_2-term of the ASS and meanwhile p · p is the first periodic element αp.    

13.  球面稳定同伦群的γ_tl_1g_0新元素族  
   王玉玉《数学年刊A辑(中文版)》,2007年第6期
   首先给出了May谱序列E_1~(s,t,u)项的几个结果,然后利用这些结果和关于Ext_P~(s,t)(Z_p,Z_p)的一个估计(P为由mod p Steenrod代数A的所有循环缩减幂P~i(i≥0)生成的子代数)得出了乘积(?)t (?)g0∈Ext_A~(*,*)(Z_p,Z_p)(3≤t    

14.  Adams谱序列上的非平凡乘积b_0k_0δ_(s+4)  
   钟立楠  刘秀贵《数学物理学报(A辑)》,2014年第34卷第2期
   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.    

15.  球面稳定同伦群的(~γ)t(~l)1g0新元素族  
   王玉玉《数学年刊A辑》,2007年第28卷第6期
   首先给出了May谱序列Es1,t,u项的几个结果,然后利用这些结果和关于ExtsP,t(Zp,Zp)的一个估计(P为由mod p Steenrod代数A的所有循环缩减幂Pi(i≥0)生成的子代数)得出了乘积~γt~l1g0∈Ext*A,*(Zp,Zp)(3≤t<p-2)在Adams谱序列的收敛性,其中g0∈Ext2A,pq+2q(Zp,Zp),~l1∈Ext3A,p2q+2pq(Zp,Zp).    

16.  A nontrivial product in the stable homotopy groups of spheres  被引次数:13
   LIU XiuguiInstitute of Mathematics  Chinese Academy of Sciences  Beijing 100080  China《中国科学A辑(英文版)》,2004年第47卷第6期
   Let A be the mod p Steenrod algebra for p an arbitrary odd prime. In 1962, Li-uleviciusdescribed hi and bk in Ext (A|*,*) (Zp, Zp) having bigrading (1,2pi(p-1))and (2,2pk+1 x(p - 1)), respectively. In this paper we prove that for p ≥ 7,n ≥ 4 and 3 ≤ s < p - 1, (Zp,Zp) survives to E∞ in the Adams spectral sequence, where q = 2(p - 1).    

17.  球面稳定同伦群的两个新元素h0(b1)3(γ)s和(b1)3g0(γ)s  
   《数学年刊A辑》,2004年第25卷第6期
   本文证明了当p(>-)11,3(<-)s<p-3时,h0(b1)3∈Ext7,3p2q+qA(H*V(2),Zp),(b1)3g0∈Ext8,3p2q+pq+2q(H*V(2),Zp)在Adams谱序列中分别收敛到π*V(2)的非零元,h0(b1)3(γ)s∈Ext7+s,(s+3)p2q+(s-1)pq+(s-3)A(Zp,Zp)在Adams谱序列中分别收敛到π*S的非零p阶元.    

18.  球面稳定同伦群的两个新元素h0(b1)3(γ)s和(b1)3g0(γ)s  
   肖建明  刘秀贵《数学年刊A辑》,2004年第25卷第6期
   本文证明了当p(>-)11,3(<-)s<p-3时,h0(b1)3∈Ext7,3p2q+qA(H*V(2),Zp),(b1)3g0∈Ext8,3p2q+pq+2q(H*V(2),Zp)在Adams谱序列中分别收敛到π*V(2)的非零元,h0(b1)3(γ)s∈Ext7+s,(s+3)p2q+(s-1)pq+(s-3)A(Zp,Zp)在Adams谱序列中分别收敛到π*S的非零p阶元.    

19.  球面稳定同伦中元素β1γs和α1γs的非平凡性  
   刘秀贵  肖建明《东北数学》,2006年第1期
   In this paper, it is proved that for p≥7 an arbitrary odd prime and 3≤s    

20.  球面稳定同伦群中的一个新元素族$b_1g_0\tilde{\gamma}_s$  
   刘秀贵《系统科学与数学》,2006年第26卷第2期
   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    

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