Steenrod代数上同调中的一个非平凡乘积元b_0~3δ_(s+4)（英文）

A NONTRIVIAL PRODUCT OF b_0~3δ_(s+4) IN THE COHOMOLOGY OF THE STEENROD ALGEBRA

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―b_0~3δ_(s+4)∈Ext_A^(s+10,t(s))(Z_p,Z_p)的非平凡性,其中p≥7,0≤s<p-5,t(s)=2(p-1)[(s+4)p^3+(s+3)p^2+(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.

In this paper,we mainly study the nontriviality of the products in the cohomology of the Steenrod algebra.Let p be a prime greater thanˉve and A be the mod p Steenrod algebra.By using the explicit combinatorial analysis of the May spectral sequence,we prove that the product b30~±s+42Exts+10;¤A(Zp;Zp)is nontrivial,where06s<p?5,which is helpful for us to study the nontriviality of homotopy elements in the stable homotopy of spheres.