模p Steenrod代数上同调的一些注记

Some Notes on the Cohomology of Mod p Steenrod Algebra

模p Steenrod代数A的上同调H^(s,t)(A)是决定球面稳定同伦群的最有力数据.首先给出了模p Steenrod代数A和May谱序列的一些重要结论,而后给出与乘积元γ_(s+3)l_ng_0∈H^(s+8,t(s,n))(A)密切相关的May谱E_1项的结果,这些结论对该乘积元的非平凡性研究有重要意义,其中t(s,n)=p^(n+1)q+2p^nq+(s+3)p^2q+(s+3)pq+(s+3)q+s, 0≤s<p-6, n≥4, p≥11, q=2(p-1).

The cohomology of the mod p Steenrod algebra A, Hs,t(A), is the most powerful data we could use to determine the stable homotopy groups of spheres. At first, this paper gives some important conclusions of Hs,t(A) and the May spectral sequence. Then we give the results of E1-term in the May spectral sequence closely related to the product elementγ^s+3lng0 ∈ Hs+8,t(s,n)(A). These conclusions have important significance for the research about the nontriviality of the product element, where t(s, n) = p^(n+1)q+2p^nq+(s + 3)p^2 q +(s + 3)pq +(s + 3)q + s, 0 ≤s < p-6, n≥4, p≥11, q = 2(p-1).