Topological representation of the geometry of metric spaces

Abstract

Inspired by the concept of hyperconvexity and its relation to curvature, we translate geometric properties of a metric space encoded by the curvature inequalities into the persistent homology induced by the Čech filtration of that space.

arXiv comment14 pages

References in corpus (2)

• Topology and curvature of metric spaces
• A notion of nonpositive curvature for general metric spaces

Cited by in corpus (1)

• Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius