{
  "id": "2407.15454",
  "version": "v1",
  "published": "2024-07-22T08:12:52.000Z",
  "updated": "2024-07-22T08:12:52.000Z",
  "title": "The Dowker theorem via discrete Morse theory",
  "authors": [
    "Morten Brun",
    "Darij Grinberg"
  ],
  "comment": "20 pages. Comments are appreciated!",
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "The Dowker theorem is a classical result in the topology of finite spaces, claiming that any binary relation between two finite spaces defines two homotopy-equivalent complexes (the Dowker complexes). Recently, Barmak strengthened this to a simple-homotopy-equivalence. We reprove Barmak's result using a combinatorial argument that constructs an explicit acyclic matching in the sense of discrete Morse theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-22T08:12:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q10",
      "55-01",
      "55U10"
    ],
    "keywords": [
      "discrete morse theory",
      "dowker theorem",
      "finite spaces defines",
      "reprove barmaks result",
      "explicit acyclic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}