{
  "id": "math/0304489",
  "version": "v2",
  "published": "2003-04-30T03:28:32.000Z",
  "updated": "2005-01-25T03:32:14.000Z",
  "title": "Belyi-extending maps and the Galois action on dessins d'enfants",
  "authors": [
    "Melanie Wood"
  ],
  "comment": "13 pages, 7 figures; submitted for publication; revisions are that the paper now deals only with Galois invariants of dessins, and that material is slightly expanded",
  "journal": "Publications of the Research Institute for Mathematical Sciences, 42 (2006), no. 3, 721--738",
  "doi": "10.2977/prims/1166642157",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study the absolute Galois group by looking for invariants and orbits of its faithful action on Grothendieck's dessins d'enfants. We define a class of functions called Belyi-extending maps, which we use to construct new Galois invariants of dessins from previously known invariants. Belyi-extending maps are the source of the ``new-type'' relations on the injection of the absolute Galois group into the Grothendieck-Teichmuller group. We make explicit how to get from a general Belyi-extending map to formula for its associated invariant which can be implemented in a computer algebra package. We give an example of a new invariant differing on two dessins which have the same values for the other readily computable invariants.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-01-25T03:32:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G32",
      "11G99",
      "14H30",
      "14G25"
    ],
    "keywords": [
      "galois action",
      "absolute galois group",
      "computer algebra package",
      "grothendiecks dessins denfants",
      "general belyi-extending map"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4489W"
    }
  }
}