{
  "id": "2108.12791",
  "version": "v1",
  "published": "2021-08-29T09:12:53.000Z",
  "updated": "2021-08-29T09:12:53.000Z",
  "title": "Arithmetic representations of mapping class groups",
  "authors": [
    "Eduard Looijenga"
  ],
  "comment": "13 p",
  "categories": [
    "math.GT",
    "math.AG",
    "math.GR"
  ],
  "abstract": "Let $S$ be a closed oriented surface and $G$ a finite group of orientation preserving automorphisms of $S$ whose orbit space has genus at least $2$. There is a natural group homomorphism from the $G$-centralizer in $Diff^+(S)$ to the $G$-centralizer in $Sp(H_1(S))$. We give a sufficient condition for its image to be a subgroup of finite index.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-29T09:12:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K20",
      "57M12",
      "11E39"
    ],
    "keywords": [
      "mapping class groups",
      "arithmetic representations",
      "natural group homomorphism",
      "orientation preserving automorphisms",
      "orbit space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}