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| 摘要: |
| 本文主要研究了Steenrod代数上同调非平凡乘积元问题.设p为大于5的素数，A代表模p的Steenrod代数.通过对May谱序列的详尽组合分析，证明了古典Admas谱序列中乘积元-b03δs+4 ∈ExtAs+10，t（s）（Zp，Zp）的非平凡性，其中p > 7，0 ≤ 6 s < p-5，t（s）=2（p-1）[（s+4）p3+（s+3）p2+（s+5）p+（s+1）]+s.这有助于对球面稳定同伦群中同伦元素非平凡性进行进一步研究. |
| 关键词: Steenrod代数 上同调 May谱序列 |
| DOI： |
| 分类号:O152.4 |
| 基金项目:Supported by the Youth Foundation of Hebei Educational Committee (QN2017505); NSFC(11571186). |
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| A NONTRIVIAL PRODUCT OF b03δs+4 IN THE COHOMOLOGY OF THE STEENROD ALGEBRA |
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WANG Chong,LIU Xiu-gui
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| Abstract: |
| In this paper, we mainly study the nontriviality of the products in the cohomology of the Steenrod algebra. Let p be a prime greater than five and A be the mod p Steenrod algebra. By using the explicit combinatorial analysis of the May spectral sequence, we prove that the product b03δs+4 ∈ ExtAs+10,*(Zp, Zp) is nontrivial, where 0 ≤ 6 s < p -5, which is helpful for us to study the nontriviality of homotopy elements in the stable homotopy of spheres. |
| Key words: Steenrod algebra cohomology May spectral sequence |
