Persistent Homotopy Groups of Metric Spaces

Facundo Mémoli; Ling Zhou

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arXiv · 1912.12399

Persistent Homotopy Groups of Metric Spaces

Facundo Mémoli·Ling Zhou

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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.

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Facundo Mémoli, Ling Zhou. 2019-12-28. Persistent Homotopy Groups of Metric Spaces. https://arxiv.org/abs/1912.12399

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