{
  "id": "1703.03393",
  "version": "v1",
  "published": "2017-03-09T18:47:03.000Z",
  "updated": "2017-03-09T18:47:03.000Z",
  "title": "Alternating links have representativity 2",
  "authors": [
    "Thomas Kindred"
  ],
  "comment": "17 pages, 14 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that if $L$ is a non-trivial alternating link embedded (without crossings) in a closed surface $F\\subset S^3$, then $F$ has a compressing disk whose boundary intersects $L$ in no more than two points. Moreover, whenever the surface is incompressible and $\\partial$-incompressible in the link exterior, it can be isotoped to have a standard tube at some crossing of any reduced alternating diagram.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-09T18:47:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "representativity",
      "boundary intersects",
      "standard tube",
      "link exterior",
      "non-trivial alternating link"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}