{
  "id": "2410.00901",
  "version": "v1",
  "published": "2024-10-01T17:45:42.000Z",
  "updated": "2024-10-01T17:45:42.000Z",
  "title": "The Complexity of Proper Homotopy Equivalence of Graphs",
  "authors": [
    "Hannah Hoganson",
    "Jenna Zomback"
  ],
  "comment": "13 pages, 12 figures",
  "categories": [
    "math.LO",
    "math.GN",
    "math.GT"
  ],
  "abstract": "We demonstrate that the proper homotopy equivalence relation for locally finite graphs is Borel complete. Furthermore, among the infinite graphs, there is a comeager equivalence class. As corollaries, we obtain the analogous results for the homeomorphism relation of noncompact surfaces with pants decompositions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-01T17:45:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "54H05",
      "57M99"
    ],
    "keywords": [
      "complexity",
      "proper homotopy equivalence relation",
      "comeager equivalence class",
      "pants decompositions",
      "borel complete"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}