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- 2018
Adams谱序列E2项的一些注记
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Abstract:
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≤s 4 )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。
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 doesnt be hitted by any element. These results are important for the detection of new family of elements in the stable homotopy groups of spheres
| [1] | 王玉玉, 王健波. 球面稳定同伦群中的<i>ξ<sub>n</sub></i>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 <i>ξ<sub>n</sub></i>-related elements in the stable homotopy groups of sphere[J]. Chinese Annals of Math(Ser A), 2014, 35(5):341-348. |
| [2] | WANG Yuyu, WANG Jianbo. The nontrivility of <i>ζ<sub>n</sub>-</i>related elements in the stable homotopy groups of sphere[J]. Math Scan, 2015, 117:304-319. |
| [3] | RAVENEL D C. Complex cobordism and stable homotopy groups of spheres[M]. Orlando: Academic Press, 1986. |
| [4] | ADAMS J F. Stable homotopy and generalised homology[M]. Chicago: University of Chicago Press, 1974. |
| [5] | 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. |
| [6] | WANG Xiangjun, ZHENG Qibing. The convergence of <i>(~overα)<sup>(n)</sup><sub>s</sub> h<sub></sub></i>0<i>h<sub>k</sub></i>[J]. Science in China, 1998, 41A(6):622-628. |
| [7] | SERRE J P. Groupes <i>d'</i> homotopie et classes de groupes abeliens[J]. Ann of Math, 1953, 58(2):258-294. |
| [8] | ADAMS J F. On the structrue and application of steerod algebra[J]. Comm Math Helv, 1958, 32(1):180-214. |
| [9] | WANG Yuyu. A new familiy of flltration <i>s</i>+5 in the stable homotopy groups of spheres[J]. Acta Math Sci, 2008, 28(2):321-332. |
