| A Nontrivial Product of Filtration s ＋ 5 in the Stable Homotopy of Spheres |
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| 引用本文： | Xiu Gui LIU. A Nontrivial Product of Filtration s ＋ 5 in the Stable Homotopy of Spheres[J]. 数学学报(英文版), 2007, 23(3): 385-392. DOI: 10.1007/s10114-005-0548-y |
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| 作者姓名： | Xiu Gui LIU |
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| 作者单位： | Department of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China |
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| 基金项目： | This paper is supported by the National Natural Science Foundation of China （No. 10501045, 10426028）, the China Postdoctoral Science Foundation and the Fund of the Personnel Division of Nankai University |
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| 摘 要： | 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）.
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| 关 键 词： | 球面 稳定同伦 非平凡积 σ域流 |
| 收稿时间： | 2003-09-15 |
| 修稿时间： | 2003-09-152004-06-28 |
A Nontrivial Product of Filtration s + 5 in the Stable Homotopy of Spheres |
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| Xiu Gui Liu. A Nontrivial Product of Filtration s + 5 in the Stable Homotopy of Spheres[J]. Acta Mathematica Sinica(English Series), 2007, 23(3): 385-392. DOI: 10.1007/s10114-005-0548-y |
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| Authors: | Xiu Gui Liu |
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| Affiliation: | (1) School of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China |
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| Abstract: | In this paper, some groups  with specialized s and t are first computed by the May spectral 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  which is represented (up to a nonzero scalar) by  in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥ 3, 0 ≤ s < p − 3, q = 2(p − 1). This paper is supported by the Youth Project of Tianyuan Foundation of China (No. 10426028), the China Postdoctoral Science Foundation and the Fund of Nankai University Personnel Division |
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| Keywords: | Stable homotopy of spheres Adams spectral sequence Toda Smith spectrum May spectral sequence |
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