论文标题
$ \ mathbb {z}/p \ times \ mathbb {z}/p $的线性动作$ s^{2n-1} \ times s^{2n-1} $
Linear actions of $\mathbb{Z}/p\times\mathbb{Z}/p$ on $S^{2n-1}\times S^{2n-1}$
论文作者
论文摘要
对于奇数$ $ p $，我们考虑$（\ mathbb {z}/p）^2 $的免费操作，$ s^{2n-1} \ times s^{2n-1} $由$（\ mathbb {z}/p）/p）的线性动作给出，$（\ mathbb {z}/p）/p）简单的示例包括镜头空间穿越镜头空间，但是$ k $ invariant的计算表明存在其他商。使用后尼科夫塔和外科理论的工具，商分类为$ k $ invariants，并由庞特拉吉金类的同态形态学。我们将介绍这些结果，并演示如何从旋转数字计算$ K $ invariants和Pontrjagin类。
For an odd prime $p$, we consider free actions of $(\mathbb{Z}/p)^2$ on $S^{2n-1}\times S^{2n-1}$ given by linear actions of $(\mathbb{Z}/p)^2$ on $\mathbb{R}^{4n}$. Simple examples include a lens space cross a lens space, but $k$-invariant calculations show that other quotients exist. Using the tools of Postnikov towers and surgery theory, the quotients are classified up to homotopy by the $k$-invariants and up to homeomorphism by the Pontrjagin classes. We will present these results and demonstrate how to calculate the $k$-invariants and the Pontrjagin classes from the rotation numbers.
