2021/11/08 by Morten Brun, Brun, Morten, Belén García Pascual +3 · 1 citation
Computer Science · Mathematics · #55N31 #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2111.04527
openalex publication_date 2021/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The homology of an unknown subspace of Euclidean space can be determined from the intrinsic Čech complex of a sample of points in the subspace, without reference to the ambient Euclidean space. More precisely, given a subspace X of Euclidean space and a sample A of points in X, we give conditions for the homology of X to be isomorphic to a certain persistent homology group of the intrinsic Čech complex.