On the asymmetry of stars at infinity
On the asymmetry of stars at infinity
复制标题
论无穷远恒星的不对称性
DOI：
10.1016/j.topol.2022.108016
复制
发表时间：
2020
影响因子：
0.6
通讯作者：
Gregory A. Kelsey
中科院分区：
文献类型：
--
作者：
K. Jones;Gregory A. Kelsey
在给定一个边界空间的情况下，卡尔松定义了无限大恒星的入射几何。当空间是双曲的、CAT(0)的或具有希尔伯特度规的有界凸区域时，这些恒星及其入射与众所周知的物体密切相关。卡尔松最初的论文提出的一个问题是，一个边界点被包含在另一个边界点的恒星中的关系是否对称。本文给出了一个例子，证明了三叉树Diestel-Leader图D，L 3(Q)的星界上的这种关系是不对称的。在此过程中，利用了Diestel-Leader图中关于距离的一些有趣的界。
Given a bordified space, Karlsson defines an incidence geometry of stars at infinity. These stars and their incidence are closely related to well-understood objects when the space is hyperbolic, CAT (0), or a bounded convex domain with the Hilbert metric. A question stemming from Karlsson's original paper was whether or not the relation of one boundary point being included in a star of another boundary point is symmetric. This paper provides an example demonstrating that this relation in the star boundary of the three-tree Diestel-Leader graph D L 3 (q) is not symmetric. In doing so, some interesting bounds on distance in Diestel-Leader graphs are utilized.