{
  "id": "1904.01945",
  "version": "v1",
  "published": "2019-04-03T12:10:48.000Z",
  "updated": "2019-04-03T12:10:48.000Z",
  "title": "Hyperbolic surfaces with sublinearly many systoles that fill",
  "authors": [
    "Maxime Fortier Bourque"
  ],
  "comment": "19 pages, 1 figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "For any $\\varepsilon>0$, we construct a closed hyperbolic surface of genus $g=g(\\varepsilon)$ with a set of at most $\\varepsilon g$ systoles that fill, meaning that each component of the complement of their union is contractible. This surface is also a critical point of index at most $\\varepsilon g$ for the systole function, disproving the lower bound of $2g-1$ conjectured by Schmutz Schaller.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-03T12:10:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "closed hyperbolic surface",
      "systole function",
      "lower bound",
      "schmutz schaller",
      "complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}