{
  "id": "1505.07944",
  "version": "v1",
  "published": "2015-05-29T07:20:46.000Z",
  "updated": "2015-05-29T07:20:46.000Z",
  "title": "Infima of length functions and dual cube complexes",
  "authors": [
    "Jonah Gaster"
  ],
  "comment": "15 pages, 6 figures, comments welcome!",
  "categories": [
    "math.GT"
  ],
  "abstract": "In the presence of certain topological conditions, we provide lower bounds for the infimum of the length function associated to a collection of curves on Teichm\\\"{u}ller space that depend on the dual cube complex associated to the collection, a concept due to Sageev. As an application of our bounds, we obtain estimates for the `longest' curve with $k$ self-intersections, complementing work of Basmajian \\cite{basmajian}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-29T07:20:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "collection",
      "dual cube complex",
      "lower bounds",
      "topological conditions",
      "length function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}