| A nontrivial product in the stable homotopy groups of spheres |
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| 作者姓名： | LIU Xiugui
Institute of Mathematics Chinese Academy of Sciences Beijing China |
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| 作者单位： | LIU Xiugui
Institute of Mathematics，Chinese Academy of Sciences，Beijing 100080，China |
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| 基金项目： | 国家自然科学基金，国家自然科学基金 |
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| 摘 要： | 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).
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A nontrivial product in the stable homotopy groups of spheres |
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| LIU Xiugui
Institute of Mathematics,Chinese Academy of Sciences,Beijing ,China.A nontrivial product in the stable homotopy groups of spheres[J].Science in China(Mathematics),2004,47(6):831-841. |
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| Authors: | Email author" target="_blank">Xiugui?LiuEmail author |
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| Institution: | Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | 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
survives to E∞ in the Adams spectral sequence, where q = 2(p — 1). |
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| Keywords: | stable homotopy groups of spheres Adams spectral sequence Toda-Smith spectra May spectral sequence |
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