Topological representation of the geometry of metric spaces

28 Jan 2020 · Joharinad Parvaneh iasbs, Jost Jürgen MPI-MIS ·

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.