{
  "id": "0808.0051",
  "version": "v2",
  "published": "2008-08-01T02:38:13.000Z",
  "updated": "2014-12-06T01:20:57.000Z",
  "title": "Birth and death in discrete Morse theory",
  "authors": [
    "Henry King",
    "Kevin Knudson",
    "Neza Mramor"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AT",
    "math.CO"
  ],
  "abstract": "Suppose $M$ is a finite simplicial complex and that for $0=t_0,t_1,...,t_r=1$ we have a discrete Morse function $F_{t_i}:M\\to \\zr$. In this paper, we study the births and deaths of critical cells for the functions $F_{t_i}$ and present an algorithm for pairing the cells that occur in adjacent slices. We first study the case where the triangulation of $M$ is the same for each $t_i$, and then generalize to the case where the triangulations may differ. This has potential applications in data imaging, where one has function values at a sample of points in some region in space at several different times or at different levels in an object.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-01T02:38:13.000Z",
      "abstract": "Suppose $M$ is a finite simplicial complex and that for $0=t_0,t_1,... ,t_r=1$ we have a discrete Morse function $F_{t_i}:M\\to \\zr$. In this paper, we study the births and deaths of critical cells for the functions $F_{t_i}$ and present an algorithm for pairing the cells that occur in adjacent slices. We first study the case where the triangulation of $M$ is the same for each $t_i$, and then generalize to the case where the triangulations may differ. This has potential applications in data imaging, where one has function values at a sample of points in some region in space at several different times or at different levels in an object.",
      "comment": "19 pages, 14 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-06T01:20:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q99",
      "68U05",
      "57R70",
      "58E05",
      "65D18",
      "65R99"
    ],
    "keywords": [
      "discrete morse theory",
      "discrete morse function",
      "finite simplicial complex",
      "function values",
      "adjacent slices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.0051K"
    }
  }
}