$H_*Ω_0^{2^{i+1}-8+k}S^{2^i-2}$的多项式子代数$η_i$族的Hurewicz象
The Hurewicz image of the $η_i$ family, a polynomial subalgebra of $H_*Ω_0^{2^{i+1}-8+k}S^{2^i-2}$
摘要：
考虑Mahowald族$η_i\in{_2π_{2^i}^S}$的Hurewicz像的计算问题.这使我们能够在$H_*Ω_0^{2^{i+1}-8+k}S^{2^i-2}$中为$0\leqslant k\leqslant 6$识别特定的球形类。然后，我们确定这些类产生的子代数的类型，并计算这些子代数的$A$ -模和$R$ -模结构。我们将讨论这些计算与$H_*Q_0S^0$中关于球类的Curtis猜想的关系，以及与$H_*Q_0S^{-n}$中球类的关系。
英文摘要：
We consider the problem of calculating the Hurewicz image of Mahowald's family $η_i\in{_2π_{2^i}^S}$. This allows us to identify specific spherical classes in $H_*Ω_0^{2^{i+1}-8+k}S^{2^i-2}$ for $0\leqslant k\leqslant 6$. We then identify the type of the subalgebras that these classes give rise to, and calculate the $A$-module and $R$-module structure of these subalgebras. We shall the discuss the relation of these calculations to the Curtis conjecture on spherical classes in $H_*Q_0S^0$, and relations with spherical classes in $H_*Q_0S^{-n}$.
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