{
  "id": "2412.16090",
  "version": "v1",
  "published": "2024-12-20T17:36:48.000Z",
  "updated": "2024-12-20T17:36:48.000Z",
  "title": "$L^2$-Betti numbers of Dehn fillings",
  "authors": [
    "Nansen Petrosyan",
    "Bin Sun"
  ],
  "comment": "53 pages, 1 figure",
  "categories": [
    "math.GR",
    "math.AT",
    "math.DG",
    "math.GT"
  ],
  "abstract": "We initiate the study of the $L^2$-Betti numbers of group-theoretic Dehn fillings. For a broad class of virtually special groups $G$, we prove that the $L^2$-Betti numbers of sufficiently deep Dehn fillings $\\overline{G}$ are equal to those of $G$. As applications, we verify the Singer Conjecture for certain Einstein manifolds, establish a virtual fibering criterion for $\\overline{G}$, obtain bounds on deficiency of $\\overline{G}$, and provide new examples of hyperbolic groups with exotic subgroups that arise as Dehn fillings of any cusped arithmetic hyperbolic manifold of dimension at least four.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-20T17:36:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "betti numbers",
      "group-theoretic dehn fillings",
      "cusped arithmetic hyperbolic manifold",
      "sufficiently deep dehn fillings",
      "virtually special groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}