共查询到19条相似文献,搜索用时 62 毫秒
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刘秀贵 《数学物理学报(A辑)》2007,27(2):208-214
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
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刘秀贵 《数学物理学报(A辑)》2007,27(2)
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
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决定球面稳定同伦群是同伦中的一个中心问题,同时也是非常困难的问题之一.Adams谱序觌是其计算的最有效的工具.在本文,令p>5为素数,A表示模p的Steenrod代数.我们利用Adams谱序列和May谱序列证明了,在球面稳定同伦群π*S中,存在一族在Adams谱序列中由b0g0γs∈Exts+4,sp2q+(s+1)pq+sq+s-3A(ZpZp)所表示的新的非平凡元素,其中q=2(p-1),3≤s相似文献
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设 $p\geq 7$ 为任意奇素数. 证明了当 $3\leq s
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设P≥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π*S中,存在由所表示的新的非平凡元素族,其中q=2(p-1),3≤s
相似文献
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刘秀贵 《数学物理学报(A辑)》2007,27(5):802-810
令 p>5 是素数, A 表示模 p Steenrod代数, S 表示球谱的 p 局部化. 首先给出了有关May谱序列的一些重要定理, 然后作为应用, 利用May谱序列和Adams谱序列发觉了一族新的非零的球面稳定元素. 该新元素族次数为2(p-1)(pn+sp2+sp+s)-7,在Adams谱序列中由 bn-1g0γs∈ ExtAs+4,﹡( ZpZp)所表示, 其中n≥4, 3≤s
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证明了在Adams谱序列中存在永久循环元hob41,且可收敛到稳定同伦群π其中V(n)是Toda-Smith谱.进而,利用Yoneda乘积,证明了在Adams谱序列中还存在永久循环元(γ)th0b41收敛到球面稳定同伦群π*(S)的一个非零元. 相似文献
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This paper computes the Thom map on γ2 and proves that it is represented by 2b2,0h1,2 in the ASS. The authors also compute the higher May differential of b2,0, from which it is proved that (~γ)s(b0hn - h1bn-1) for 2 ≤ s < p - 1 are permanent cycles in the ASS. 相似文献
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Xiugui LIU Xiangjun WANG Department of Mathematics LPMC Nankai University Tianjin China. 《数学年刊B辑(英文版)》2006,(3)
This paper computes the Thorn map onγ2 and proves that it is represented by 2b2,0h1,2 in the ASS. The authors also compute the higher May differential of 62,0, from which it is proved thatγs(b0hn-h1bn-1) for 2≤s < p - 1 are permanent cycles in the ASS. 相似文献
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Abstract This paper computes the Thom map on γ2 and proves that it is represented by 2b2,0h1,2 in the ASS. The authors also compute the higher May differential of b2,0, from which it is proved that
for 2 ≤ s < p - 1 are permanent cycles in the ASS.
* Project supported by the National Natural Science Foundation of China (No.10501045), the Tianyuan Foundation of Mathematics
(No.10426028) and the Fund of the Personnel Division of Nankai University. 相似文献
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令p是一个大于5的奇素数.本文证明了在收敛到Moore谱的稳定同伦群的Adams谱序列中,在相差一个非零系数下,h_2的2p阶Adams微分是a_1b_0~p. 相似文献
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In this paper, a new family of homotopy elements in the stable homotopy groups of spheres represented by
in the Adams spectral sequence is detected, where n − 2 ≥ m ≥ 5 and 3 ≤ s < p. 相似文献
n−2≥m≥5 and 3≤s<p.
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In this paper, we introduce a four-filtrated version of the May spectral sequence (MSS), from which we study the general properties
of the spectral sequence and give a collapse theorem. We also give an efficient method to detect generators of May E
1-term E
1
s,t,b,*
for a given (s, t, b, *). As an application, we give a method to prove the non-triviality of some compositions of the known homotopy elements in
the classical Adams spectral sequence (ASS).
This research is partially supported by the National Natural Science Foundation of China (Nos. 10501045, 10771105) and the
Fund of the Personnel Division of Nankai University 相似文献
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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
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Xiu Gui LIU 《数学学报(英文版)》2007,23(6):1025-1032
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
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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]. 相似文献