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山东大学学报(理学版) ›› 2018, Vol. 53 ›› Issue (8): 43-48.doi: 10.6040/j.issn.1671-9352.0.2017.383

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Adams谱序列E2项的一些注记

刘艳芳,王玉玉*   

  1. 天津师范大学数学科学学院, 天津 300387
  • 收稿日期:2017-07-31 出版日期:2018-08-20 发布日期:2018-07-11
  • 作者简介:刘艳芳(1991— ),男,硕士研究生,研究方向为稳定同伦论. E-mail:1808861603@qq.com*通信作者简介:王玉玉(1979— ),女,博士,研究员,硕士生导师,研究方向为同伦论. E-mail:wdoubleyu@aliyun.com
  • 基金资助:
    国家自然科学基金资助项目(11301386)

Some notes on E2-term of Adams spectral sequence

LIU Yan-fang, WANG Yu-yu*   

  1. College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
  • Received:2017-07-31 Online:2018-08-20 Published:2018-07-11

摘要: 利用May谱序列的相关理论对Adams谱序列的E2项,即模p Steenrod代数A的上同调进行讨论。具体给出了(~overγ)s+3b1hn(n≥4, 0≤s4)在Adams谱序列中的非平凡性,并且说明其不是任何元素微分的像。这些结论对球面稳定同伦群新元素的发掘具有重要意义。

关键词: Adams微分, May微分, Ext群, May谱序列, 非平凡性

Abstract: The E2-term of the Adams spectral sequence, which is the cohomology of mod p Steenrod algebra A, will be discussed by using the May spectral sequence. In the Adams spectral sequence, the non-triviality of (~overγ)s+3b1hn is given, and it doesnt be hitted by any element. These results are important for the detection of new family of elements in the stable homotopy groups of spheres.

Key words: Ext group, non-triviality, May spectral sequence, May differential, Adams differential

中图分类号: 

  • O189.23
[1] SERRE J P. Groupes d' homotopie et classes de groupes abeliens[J]. Ann of Math, 1953, 58(2):258-294.
[2] ADAMS J F. On the structrue and application of steerod algebra[J]. Comm Math Helv, 1958, 32(1):180-214.
[3] ADAMS J F. Stable homotopy and generalised homology[M]. Chicago: University of Chicago Press, 1974.
[4] ZHONG Linan, WANG Yuyu. Detection of a nontrivial product in the stable homotopy groups of spheres[J]. Algebr Geom Topol, 2013, 13(5):3009-3029.
[5] 王玉玉, 王健波. 球面稳定同伦群中的ξn相关元素的非平凡性[J]. 数学年刊(A辑), 2014, 35(5):341-348. WANG Yuyu, WANG Jianbo. The nontriviality of ξn-related elements in the stable homotopy groups of sphere[J]. Chinese Annals of Math(Ser A), 2014, 35(5):341-348.
[6] WANG Yuyu, WANG Jianbo. The nontrivility of ζn-related elements in the stable homotopy groups of sphere[J]. Math Scan, 2015, 117:304-319.
[7] RAVENEL D C. Complex cobordism and stable homotopy groups of spheres[M]. Orlando: Academic Press, 1986.
[8] WANG Yuyu. A new familiy of flltration s+5 in the stable homotopy groups of spheres[J]. Acta Math Sci, 2008, 28(2):321-332.
[9] WANG Xiangjun, ZHENG Qibing. The convergence of (~overα)(n)s h0hk[J]. Science in China, 1998, 41A(6):622-628.
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