{
  "id": "0712.1625",
  "version": "v1",
  "published": "2007-12-11T01:49:25.000Z",
  "updated": "2007-12-11T01:49:25.000Z",
  "title": "Bridge Number and Conway Products",
  "authors": [
    "Ryan C. Blair"
  ],
  "comment": "15 pages, 13 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Schubert proved that, given a composite link $K$ with summands $K_{1}$ and $K_{2}$, the bridge number of $K$ satisfies the following equation: $$\\beta(K)=\\beta(K_{1})+\\beta(K_{2})-1.$$ In ``Conway Produts and Links with Multiple Bridge Surfaces\", Scharlemann and Tomova proved that, given links $K_{1}$ and $K_{2}$, there is a Conway product $K_{1}\\times_{c}K_{2}$ such that $$\\beta(K_{1}\\times_{c} K_{2}) \\leq \\beta(K_{1}) + \\beta(K_{2}) - 1$$ In this paper, we define the generalized Conway product $K_{1}\\ast_{c}K_{2}$ and prove the lower bound $\\beta(K_{1}\\ast_{c}K_{2}) \\geq \\beta(K_{1})-1$ where $K_{1}$ is the distinguished factor of the generalized product. We go on to show this lower bound is tight for an infinite class of links with arbitrarily high bridge number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-11T01:49:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bound",
      "multiple bridge surfaces",
      "arbitrarily high bridge number",
      "conway produts",
      "composite link"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.1625B"
    }
  }
}