论文标题
组合标准和欧几里得空间准时阶段的中心
A Combinatorial Criterion and Center for the quasi-isometry groups of Euclidean spaces
论文作者
论文摘要
在这项研究中，我们介绍了$pl_Δ$ - 瘤的概念，$ \ mathbb {r}^n $。此外，我们提供了一个依赖于简单结构的顶点和边缘的组合标准，以确定分段线性同构形态是否为准等级法。通过采用此标准，我们随后表明，组$ qi的中心（\ mathbb {r}^n）$，它包括$ \ mathbb {r}^n $的所有Quasi ismoteries，确实是微不足道的。
In this study, we introduce the notion of $PL_δ$-homeomorphisms of $\mathbb{R}^n$. Furthermore, we provide a combinatorial criterion reliant on the vertices and edges of simplicial structures, to determine whether a piecewise-linear homeomorphism to be a quasi-isometry. By employing this criterion, we subsequently show that the center of the group $QI(\mathbb{R}^n)$, which comprises all quasi-isometries of $\mathbb{R}^n$, is indeed trivial.
