{
  "id": "0706.2608",
  "version": "v1",
  "published": "2007-06-18T19:42:00.000Z",
  "updated": "2007-06-18T19:42:00.000Z",
  "title": "A refinement of multi-dimensional persistence",
  "authors": [
    "Kevin P. Knudson"
  ],
  "comment": "21 pages, 4 figures",
  "categories": [
    "math.AT"
  ],
  "abstract": "We study the multi-dimensional persistence of Carlsson and Zomorodian and obtain a finer classification based upon the higher tor-modules of a persistence module. We propose a variety structure on the set of isomorphism classes of these modules, and present several examples. We also provide a geometric interpretation for the higher tor-modules of homology modules of multi-filtered simplicial complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-18T19:42:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-dimensional persistence",
      "refinement",
      "higher tor-modules",
      "homology modules",
      "geometric interpretation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.2608K"
    }
  }
}