{
  "id": "1210.4097",
  "version": "v1",
  "published": "2012-10-15T16:31:08.000Z",
  "updated": "2012-10-15T16:31:08.000Z",
  "title": "A subset of Euclidean space with large Vietoris-Rips homology",
  "authors": [
    "Jean-Marie Droz"
  ],
  "comment": "3 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We construct a compact subset K of the four dimensional Euclidean space with the following property: For all values of the parameter in an interval, the Vietoris-Rips complex of K has uncountably generated first homology. This answers a question that arose in work on persistent homology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-15T16:31:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N99"
    ],
    "keywords": [
      "large vietoris-rips homology",
      "dimensional euclidean space",
      "compact subset",
      "uncountably generated first homology",
      "persistent homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.4097D"
    }
  }
}