{
  "id": "2309.07095",
  "version": "v1",
  "published": "2023-09-13T17:13:08.000Z",
  "updated": "2023-09-13T17:13:08.000Z",
  "title": "Directed Homology and Persistence Modules",
  "authors": [
    "Eric Goubault"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "In this note, we give a self-contained account on a construction for a directed homology theory based on modules over algebras, linking it to both persistence homology and natural homology. We study its first properties, among which some exact sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-13T17:13:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "persistence modules",
      "exact sequences",
      "directed homology theory",
      "persistence homology",
      "natural homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}