{
  "id": "1603.07406",
  "version": "v1",
  "published": "2016-03-24T01:26:35.000Z",
  "updated": "2016-03-24T01:26:35.000Z",
  "title": "Higher interpolation and extension for persistence modules",
  "authors": [
    "Peter Bubenik",
    "Vin de Silva",
    "Vidit Nanda"
  ],
  "comment": "12 Pages, 2 Figures",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "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. As a consequence of such \"higher-interpolation\", it becomes possible to compare Vietoris-Rips and Cech complexes built within the space of persistence modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-24T01:26:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "persistence modules",
      "higher interpolation",
      "coherence criterion",
      "larger ambient metric spaces",
      "contemporary data analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160307406B"
    }
  }
}