论文标题
半均匀空间的越野河流同源理论
Vietoris-Rips Homology Theory for Semi-Uniform Spaces
论文作者
论文摘要
虽然越越野杆络合物现在广泛用于拓扑数据分析和双曲线群的理论，但其同源性的许多基本特性仍然难以捉摸。在本文中，我们为半均匀空间定义了越野式 - 核糖的同源性，该空间概括了图形和度量空间的经典理论，并为构造提供了自然的一般环境。然后，我们在这种情况下证明了Eilenberg-Steenrod公理的一个版本，在此过程中为半均匀空间提供了同型的自然定义。
While the Vietoris-Rips complex is now widely used in both topological data analysis and the theory of hyperbolic groups, many of the fundamental properties of its homology have remained elusive. In this article, we define the Vietoris-Rips homology for semi-uniform spaces, which generalizes the classical theory for graphs and metric spaces, and provides a natural, general setting for the construction. We then prove a version of the Eilenberg-Steenrod axioms in this setting, giving a natural definition of homotopy for semi-uniform spaces in the process.
