On the Convergence of Products $$ \ifmmode\expandafter\tilde\else\expandafter\~\fi{\gamma }_{s} h_{1} h_{n} $$ in the Adams Spectral Sequence
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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DOI：
10.1007/s10114-005-0863-3
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发表时间：
2007-06
期刊：
影响因子：
--
通讯作者：
X. Liu
中科院分区：
文献类型：
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作者：
X. Liu
LetAbe the modpSteenrod algebra andSthe sphere spectrum localized atp, wherepis an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented byin the Adams spectral sequence. At the same time, he proved thatis 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 $$ j{j}\ifmmode{'}\else$'$\fi\overline{j} \gamma ^{s} \overline{i} {i}\ifmmode{'}\else$'$\fi\xi _{n} $$ in the stable homotopy groups of spheres. The new one is of degreepnq+sp2q+spq+ (s− 2)q+s− 6 and is represented up to a nonzero scalar by $$ h_{1} h_{n} \ifmmode\expandafter\tilde\else\expandafter\~\fi{\gamma }_{s} $$ in theof the Adams spectral sequence, wherep≥ 7,q= 2(p− 1),n≥ 4 and 3 ≤s<p.
LetAbe the modpSteenrod algebra andSthe sphere spectrum localized atp, wherepis an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented byin the Adams spectral sequence. At the same time, he proved thatis 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 $$ j{j}\ifmmode{'}\else$'$\fi\overline{j} \gamma ^{s} \overline{i} {i}\ifmmode{'}\else$'$\fi\xi _{n} $$ in the stable homotopy groups of spheres. The new one is of degreepnq+sp2q+spq+ (s− 2)q+s− 6 and is represented up to a nonzero scalar by $$ h_{1} h_{n} \ifmmode\expandafter\tilde\else\expandafter\~\fi{\gamma }_{s} $$ in theof the Adams spectral sequence, wherep≥ 7,q= 2(p− 1),n≥ 4 and 3 ≤s<p.