{
  "id": "2103.06408",
  "version": "v1",
  "published": "2021-03-11T01:46:13.000Z",
  "updated": "2021-03-11T01:46:13.000Z",
  "title": "Geometric Approaches on Persistent Homology",
  "authors": [
    "Henry Adams",
    "Baris Coskunuzer"
  ],
  "categories": [
    "math.AT",
    "cs.CG",
    "math.GN"
  ],
  "abstract": "We introduce several geometric notions, including thick-thin decompositions and the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the \"size\" or \"persistence\" of a homology class. As a case study, we analyze the power filtration on unweighted graphs, and provide explicit bounds for the life spans of homology classes in persistence diagrams in all dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-11T01:46:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "persistent homology",
      "geometric approaches",
      "homology class",
      "persistence diagrams",
      "geometric descriptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}