{
  "id": "1108.5640",
  "version": "v1",
  "published": "2011-08-29T16:33:25.000Z",
  "updated": "2011-08-29T16:33:25.000Z",
  "title": "Bridge number and tangle products",
  "authors": [
    "Ryan Blair"
  ],
  "comment": "13 pages, 11 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that essential punctured spheres in the complement of links with distance three bridge spheres have bounded complexity. We define the operation of tangle product, a generalization of both connected sum and Conway product. Finally, we use the bounded complexity of essential punctured spheres to show that the bridge number of a tangle product is at least the sum of the bridge numbers of the two factor links up to a constant error.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-29T16:33:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57M50"
    ],
    "keywords": [
      "bridge number",
      "tangle product",
      "essential punctured spheres",
      "bounded complexity",
      "factor links"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.5640B"
    }
  }
}