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Adams谱序列中的2个非零微分

Two Nontrivial Differentials in the Adams Spectral Sequence
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摘要 利用关于Ext_P^(*,*)(Z_p,Z_p)的一个估计,算出了Toda谱V(n)的某些特殊维数和次数上的Ext群的生成元情况,然后根据这几个结果并利用Adams谱序列和May谱序列作为工具,得出了i_i′i_*(g_1),i_*(g_1)的非零微分及不收敛性,最后得到了π_*V(1)中元素i′j′βi′与■的一组关系式. By means of an estimate of Ext^8,5p (Zp, Zp), some Ext groups of the Toda spectrum in some special dimensions and degrees are obtained. Then two new nontrivial differentials are detected by the Adams spectral sequence and the may spectral sequence. Finally, the relation μ(i'j'βi'i∧-↑jγ-↑ii'i) ≠ 0 in π*V(1) is given.
作者 高曼
机构地区 南开大学数学系
出处 《数学年刊(A辑)》 CSCD 北大核心 2008年第5期725-736,共12页 Chinese Annals of Mathematics
关键词 ADAMS谱序列 MAY谱序列 Toda谱V(n) Adams—Novibv谱序列 Adams spectral sequence, May spectral sequence, Toda spectrum V(n), Adams-Novikov spectral sequence
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参考文献5

  • 1Toda H., On spectra realizing exterior part of the Steenrod algebra [J], Topology, 1971, 10:53-65.
  • 2Ravenel D. C., Complex cobordism and stable homotopy groups of spheres [M]//Pure and Applied Mathematics, 121, Orlando, FL: Academic Press, Inc., 1986.
  • 3Oka S., Multiplicative structure of finite ring spectra and stable homotopy of spheres [M]// Algebraic Topology (Aarhus), Lect. Notes in Math. V. 1051, Berlin: Springer-Verlag, 1984:419- 441.
  • 4Miller H. R. and Wilson W. S., On Novikov's Ext^1 modulo an invariant prime ideal [J], Topology, 1976, 15:131-141.
  • 5Miller H. R., Ravenel D. C. and Wilson W. S., Periodic phenomena in the Adams- Novikov spectral sequence [J], Ann. of Math., 1977, 106:469-516.

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