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A subset of Euclidean space with large Vietoris-Rips homology

2012/10/15 by Jean-Marie Droz, Droz, Jean-Marie
Computer Science · Mathematics · #55N99 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1210.4097

openalex publication_date 2012/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a compact subset K of the four dimensional Euclidean space with the following property: For all values of the parameter in an interval, the Vietoris-Rips complex of K has uncountably generated first homology. This answers a question that arose in work on persistent homology.

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