Persistent Homotopy Groups of Metric Spaces

2019/12/28 by Mémoli, Facundo, Zhou, Ling · 3 citations
#51F99 #53C23 #55N35 #Algebraic Topology (math.AT) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.12399

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.

Cited by

• Biclosed monoidal structures on the categories of digraphs and graphs
• Persistence and Topological Complexity
• Data analysis using discrete cubical homology

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