{
  "id": "2407.18029",
  "version": "v1",
  "published": "2024-07-25T13:26:09.000Z",
  "updated": "2024-07-25T13:26:09.000Z",
  "title": "Nearly-linear solution to the word problem for 3-manifold groups",
  "authors": [
    "Alessandro Sisto",
    "Stefanie Zbinden"
  ],
  "comment": "24 pages, 1 figure",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We show that the word problem for any 3-manifold group is solvable in time $O(n\\log^3 n)$. Our main contribution is the proof that the word problem for admissible graphs of groups, in the sense of Croke and Kleiner, is solvable in $O(n\\log n)$; this covers fundamental groups of non-geometric graph manifolds. Similar methods also give that the word problem for free products can be solved \"almost as quickly\" as the word problem in the factors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-25T13:26:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "word problem",
      "nearly-linear solution",
      "non-geometric graph manifolds",
      "covers fundamental groups",
      "main contribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}