Topological representation of the geometry of metric spaces

Published 28 Jan 2020 in math.GT and math.MG | (2001.10262v1)

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 \v{C}ech filtration of that space.

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