论文标题
关于$ p $ adadic simplicial卷的注释
A note on $p$-adic simplicial volumes
论文作者
论文摘要
我们定义并研究了简单量的概括，而不是任意的半态环，重点是$ p $ adadic simplicial卷。我们研究对质量的依赖性，并根据$ p $ ad的简单量建立同源界限。作为主要示例，我们计算了表面的失重和$ p $ - 亚法的简单卷。这提供了一种方法，可以计算经典的简单量的表面，而无需双曲线拉直，并表明表面满足mod $ p $和$ p $ - 亚法的简单量近似。
We define and study generalizations of simplicial volume over arbitrary seminormed rings with a focus on $p$-adic simplicial volumes. We investigate the dependence on the prime and establish homology bounds in terms of $p$-adic simplicial volumes. As the main examples we compute the weightless and $p$-adic simplicial volumes of surfaces. This gives a way to calculate classical simplicial volume of surfaces without hyperbolic straightening and shows that surfaces satisfy mod $p$ and $p$-adic approximation of simplicial volume.
