{
  "id": "1207.3493",
  "version": "v1",
  "published": "2012-07-15T11:19:54.000Z",
  "updated": "2012-07-15T11:19:54.000Z",
  "title": "Codes for Square-Tiled Surfaces",
  "authors": [
    "Kuo-Chiang Tan"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we use permutation elements to record cylinder decompositions of a square-tiled surface $X$. Collecting all such possible permutation elements that record cylinder decompositions, we can enumerate the $SL_2(\\mathbb{Z})$ orbit of a given surface $X$ and give a method to determine whether or not a matrix $A\\in SL_2(\\mathbb{Z})$ is the differential of an affine diffeomorphism of $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-15T11:19:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "square-tiled surface",
      "record cylinder decompositions",
      "permutation elements",
      "affine diffeomorphism",
      "differential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.3493T"
    }
  }
}