The Vietoris–Rips complexes of a circle
The Vietoris–Rips complexes of a circle
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 Jean-Claude Hausmann states that if X is a Riemannian manifold and r is sufficiently small, then the Vietoris-Rips …