The Vietoris-Rips complexes of a circle

Abstract

Given a metric space X and a distance threshold r > 0, the Vietoris–Rips simplicial complex has as its simplices the finite subsets of X of diameter less than r. A theorem of JeanClaude Hausmann states that if X is a Riemannian manifold and r is sufficiently small, then the Vietoris–Rips complex is homotopy equivalent to the original manifold. Little is… (More)
DOI: 10.2140/pjm.2017.290.1

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