Acta mathematica scientia,Series B
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Liu Xiugui
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Abstract:
In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres $\pi_{t-6}S$ which is represented by $h_ng_0\tilde{\gamma}_{3} \in {\rm Ext}_A^{6,t}(Z_p,Z_p)$ 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 $\pi_{t_1-s-6}S$ which is represented by $h_ng_0\tilde{\gamma}_{s+3}\in {\rm Ext}_A^{s+6,t_1}(Z_p,Z_p)$ in the Adams spectral sequence, where n≥4, 0≤ s< p-4, t1=2pn(p-1)+2(p-1)((s+3)p2+(s+3)p+(s+3))+s.
Key words: Stable homotopy groups of spheres, Adams spectral sequence, Toda-Smith spectrum, May spectral sequence
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Liu Xiugui. A NEW FAMILY OF FILTRATION s+6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES[J].Acta mathematica scientia,Series B, 2006, 26(2): 193-201.
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URL: http://121.43.60.238/sxwlxbB/EN/10.1016/S0252-9602(06)60041-6
http://121.43.60.238/sxwlxbB/EN/Y2006/V26/I2/193
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