Title: Persistent homotopy groups of metric spaces
Abstract: By capturing both geometric and topological features of datasets, persistent homology has increasingly been used in applications. Motivated by the fact that usually homotopy groups contain more information than homology groups, we study notions of persistent homotopy groups of compact metric spaces, together with their stability properties in the Gromov-Hausdorff sense. We show that in analogy with hierarchical clustering, under fairly mild assumptions on the spaces, the classical fundamental group, isomorphic to the limit of the persistent fundamental group, admits via our persistent lens an underlying tree-like structure (i.e. a dendrogram) and an associated ultrametric.
The paper discussed in this talk is available on arXiv: https://arxiv.org/abs/1912.12399
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