{
  "id": "2310.07024",
  "version": "v1",
  "published": "2023-10-10T21:24:19.000Z",
  "updated": "2023-10-10T21:24:19.000Z",
  "title": "Computing the twisted $L^2$-Euler characteristic",
  "authors": [
    "Jacopo G. Chen"
  ],
  "comment": "55 pages, 5 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We present an algorithm that computes Friedl and L\\\"uck's twisted $L^2$-Euler characteristic for a suitable regular CW complex, employing Oki's matrix expansion algorithm to indirectly evaluate the Dieudonn\\'e determinant. The algorithm needs to run for an extremely long time to certify its outputs, but a truncated, human-assisted version produces very good results in many cases, such as hyperbolic link complements, closed census 3-manifolds, free-by-cyclic groups, and higher-dimensional examples, such as the fiber of the Ratcliffe-Tschantz manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-10T21:24:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euler characteristic",
      "employing okis matrix expansion algorithm",
      "hyperbolic link complements",
      "suitable regular cw complex",
      "algorithm needs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}