# Persistent Homotopy Groups of Metric Spaces

arXiv: https://arxiv.org/abs/1912.12399 · HTML: https://mlsanity.com/paper/1912.12399/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2019.

## Built on by (most cited first, 1 of 1)

- [Topological data analysis using persistent discrete homology](https://mlsanity.com/paper/2506.15020/) (2025)

## Abstract (arXiv)

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.