{
  "id": "1505.07171",
  "version": "v1",
  "published": "2015-05-27T01:31:34.000Z",
  "updated": "2015-05-27T01:31:34.000Z",
  "title": "Bounds on the number of non-simple closed geodesics on a surface",
  "authors": [
    "Jenya Sapir"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We give bounds on the number of non-simple closed curves on a negatively curved surface, given upper bounds on both length and self-intersection number. In particular, it was previously known that the number of all closed curves of length at most $L$ grows exponentially in $L$. We get exponentially tighter bounds given weak conditions on self-intersection number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-27T01:31:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-simple closed geodesics",
      "self-intersection number",
      "upper bounds",
      "non-simple closed curves",
      "exponentially tighter bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150507171S"
    }
  }
}