Persistent Homotopy Groups of Metric Spaces

Abstract

We study notions of persistent homotopy groups of compact metric spaces together with their stability properties in the Gromov-Hausdorff sense. We pay particular attention to the case of fundamental groups, for which we obtain a more precise description. Under fairly mild assumptions on the spaces, we proved that the classical fundamental group has an underlying tree-like structure (i.e. a dendrogram) and an associated ultra-metric.

60 pages (not counting appendices)

References in corpus (5)

• Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
• The Metric Space of Networks
• Persistent homotopy theory
• Fundamental groups as limits of discrete fundamental groups
• Data and homotopy types