Persistent Homotopy Groups of Metric Spaces
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.
PDF AbstractCategories
Algebraic Topology
Computational Geometry
53C23, 51F99, 55N35
