{
  "id": "1305.0993",
  "version": "v1",
  "published": "2013-05-05T09:08:46.000Z",
  "updated": "2013-05-05T09:08:46.000Z",
  "title": "Sofic profile and computability of Cremona groups",
  "authors": [
    "Yves Cornulier"
  ],
  "comment": "20 pages, no figure",
  "journal": "Michigan Math. J. 62(4) (2013) 823-841",
  "doi": "10.1307/mmj/1387226167",
  "categories": [
    "math.GR",
    "math.AG"
  ],
  "abstract": "In this paper, we show that Cremona groups are sofic. We actually introduce a quantitative notion of soficity, called sofic profile, and show that the group of birational transformations of a d-dimensional variety has sofic profile at most polynomial of degree d. We also observe that finitely generated subgroups of the Cremona group have a solvable word problem. This provides examples of finitely generated groups with no embeddings into any Cremona group, answering a question of S. Cantat.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-05T09:08:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E07",
      "20B99",
      "20F10",
      "12E20"
    ],
    "keywords": [
      "cremona group",
      "sofic profile",
      "computability",
      "d-dimensional variety",
      "solvable word problem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.0993C"
    }
  }
}