{
  "id": "2001.10262",
  "version": "v1",
  "published": "2020-01-28T11:07:26.000Z",
  "updated": "2020-01-28T11:07:26.000Z",
  "title": "Topological representation of the geometry of metric spaces",
  "authors": [
    "Parvaneh Joharinad",
    "Jürgen Jost"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GT",
    "math.MG"
  ],
  "abstract": "Inspired by the concept of hyperconvexity and its relation to curvature, we translate geometric properties of a metric space encoded by the curvature inequalities into the persistent homology induced by the \\v{C}ech filtration of that space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-28T11:07:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51Fxx",
      "14Fxx",
      "G.2.m"
    ],
    "keywords": [
      "metric space",
      "topological representation",
      "translate geometric properties",
      "persistent homology",
      "curvature inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}