Topological representation of the geometry of metric spaces

2020/01/28 by Joharinad, Parvaneh, Jost, Jürgen
#14Fxx #51Fxx #FOS: Mathematics #G.2.m #Geometric Topology (math.GT) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2001.10262

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.

Related

• Geometric Bounds for Persistence
• Elementary aspects of the geometry of metric spaces
• Curvature Sets Over Persistence Diagrams
• A Topological Study of Functional Data and Fréchet Functions of Metric Measure Spaces
• Dimensionality Reduction for k-Distance Applied to Persistent Homology