{
  "id": "2202.03159",
  "version": "v1",
  "published": "2022-02-07T13:36:08.000Z",
  "updated": "2022-02-07T13:36:08.000Z",
  "title": "$L^2$-Betti numbers and computability of reals",
  "authors": [
    "Clara Loeh",
    "Matthias Uschold"
  ],
  "comment": "35 pages; Lean implementation available at https://gitlab.com/L2-comp/l2-comp-lean",
  "categories": [
    "math.GR",
    "cs.LO",
    "math.GT",
    "math.LO"
  ],
  "abstract": "We study the computability degree of real numbers arising as $L^2$-Betti numbers or $L^2$-torsion of groups, parametrised over the Turing degree of the word problem. Moreover, we explain how such considerations can be modelled in a proof assistant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-07T13:36:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "betti numbers",
      "computability degree",
      "word problem",
      "proof assistant",
      "turing degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}