{
  "id": "2210.12868",
  "version": "v1",
  "published": "2022-10-23T22:05:11.000Z",
  "updated": "2022-10-23T22:05:11.000Z",
  "title": "Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values",
  "authors": [
    "Asilata Bapat",
    "Robyn Brooks",
    "Celia Hacker",
    "Claudia Landi",
    "Barbara I. Mahler",
    "Elizabeth R. Stephenson"
  ],
  "comment": "28 pages, 6 figures. Comments welcome",
  "categories": [
    "math.AT",
    "cs.CG"
  ],
  "abstract": "The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would allow multi-parameter persistent homology to be a viable option for data analysis. In this paper, we provide theoretical results for the computation of the matching distance in two dimensions along with a geometric interpretation of the lines through parameter space realizing this distance. The crucial point of the method we propose is that it can be easily implemented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-23T22:05:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N31",
      "62R40"
    ],
    "keywords": [
      "matching distance",
      "critical values",
      "multi-parameter persistence modules",
      "multi-parameter persistent homology",
      "crucial point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}