关于博特周期性、$H_*QX$中的$\mathcal{A}$ -湮没类和稳定对称命中问题
On the Bott periodicity, $\mathcal{A}$-annihilated classes in $H_*QX$, and the stable symmetric hit problem
摘要：
当$X$是某个路连通空间时，我们给出了同调环$H_*(QX;\mathbb{Z}/2)$和$H_*(Q(X_+);\mathbb{Z}/2)$中$\mathcal{A}$ -零化生成元的一个刻画.我们还介绍了一种方法来构造这样的类。我们评论这个结果的应用，以说明如何使用$\mathbb{Z}\times BO$上的无限循环空间结构，提供的博特周期性可以用来获得一些信息的（稳定）对称击中问题的木材和Janfada。我们的方法似乎允许许多简单的计算。我们定理3的数值条件看起来非常类似于Wood \cite{Wood-Ioa}和Janfada-Wood \cite{JanfadaWood}以及Janfada \cite{Janfada-P(3)}所考虑的“尖峰”。
英文摘要：
We provide a characterisation of $\mathcal{A}$-annihilated generators in the homology ring $H_*(QX;\mathbb{Z}/2)$ and $H_*(Q(X_+);\mathbb{Z}/2)$ when $X$ is some path connected space. We also introduce a method to construct such classes. We comment on the application of this result to illustrate how to use the infinite loop space structure on $\mathbb{Z}\times BO$, provided by the Bott periodicity can be used to obtain some information on the (stable) symmetric hit problem of Wood and Janfada. Our methods seem to allow much straightforward calculations. The numerical conditions of our Theorem 3 look very similar to the `spikes' considered by Wood \cite{Wood-Ioa} and Janfada-Wood \cite{JanfadaWood} as well as Janfada \cite{Janfada-P(3)}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
