{
  "id": "2205.06155",
  "version": "v1",
  "published": "2022-05-12T15:26:46.000Z",
  "updated": "2022-05-12T15:26:46.000Z",
  "title": "Pro-$p$ completions of $PD_n$-groups",
  "authors": [
    "Jonathan Hillman",
    "Dessislava H. Kochloukova"
  ],
  "comment": "Some of the results of the final section are based on arXiv 1305.3953 [math.GT]",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We sharpen earlier work on the pro-$p$ completions of orientable $PD_3$-groups. There are four cases, and we give examples of aspherical 3-manifolds representing each case. In three of the four cases the new results are best possible. We also consider the pro-$p$ completion of some orientable $PD_n$ groups for $n \\leq 5$, including surface-by-surface groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-12T15:26:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "completion",
      "sharpen earlier work",
      "surface-by-surface groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}