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- W2308099041 abstract "The use of topological persistence in contemporary data analysis has provided considerable impetus for investigations into the geometric and functional-analytic structure of the space of persistence modules. In this paper, we isolate a coherence criterion which guarantees the extensibility of non-expansive maps into this space across embeddings of the domain to larger ambient metric spaces. Our coherence criterion is category-theoretic, allowing Kan extensions to provide the desired extensions. Our main construction gives an isometric embedding of a metric space into the metric space of persistence modules with values in the spacetime of this metric space. As a consequence of such higher interpolation, it becomes possible to compare Vietoris-Rips and v{C}ech complexes built within the space of persistence modules." @default.
- W2308099041 created "2016-06-24" @default.
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- W2308099041 date "2017-01-01" @default.
- W2308099041 modified "2023-10-16" @default.
- W2308099041 title "Higher Interpolation and Extension for Persistence Modules" @default.
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- W2308099041 doi "https://doi.org/10.1137/16m1100472" @default.
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