2020/08/13 by Antonio Rieser, Rieser, Antonio
Computer Science · Mathematics · Medicine · #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Leprosy Research and Treatment #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2008.05739
openalex publication_date 2020/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.