| On the Convergence of Products γ^-sh1hn in the Adams Spectral Sequence |
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| 作者姓名： | Xiu Gui LIU |
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| 作者单位： | School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P.R. China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （No. 10501045, 10426028）, the China Postdoc- toral Science Foundation and the Fund of the Personnel Division of Nankai University |
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| 摘 要： | 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.
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| 关 键 词： | 同伦群 球面 稳定性 Adams光谱序列 May光谱序列 |
| 修稿时间： | 2004-05-212005-01-11 |
On the Convergence of Products $$
\ifmmode\expandafter\tilde\else\expandafter\~\fi{\gamma }_{s} h_{1} h_{n}
$$ in the Adams Spectral Sequence |
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| Xiu Gui LIU.On the Convergence of Products $$
\ifmmode\expandafter\tilde\else\expandafter\~\fi{\gamma }_{s} h_{1} h_{n}
$$ in the Adams Spectral Sequence[J].Acta Mathematica Sinica,2007,23(6):1025-1032. |
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| Authors: | Xiu Gui Liu |
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| Institution: | (1) School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China |
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| 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
in the Adams spectral sequence. At the same
time, he proved that
is a permanent cycle in the Adams spectral
sequence and converges to a nontrivial element
. 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
in the stable homotopy groups of spheres. The new one is of
degree p
n
q + sp
2
q + spq + (s − 2)q + s − 6 and is represented up to a nonzero scalar by
in the
of the Adams spectral sequence, where p ≥ 7, q = 2(p − 1), n ≥ 4 and 3 ≤ s < p.
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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| Keywords: | stable homotopy groups of spheres Adams spectral sequence May spectral sequence |
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