{
  "id": "1604.04273",
  "version": "v1",
  "published": "2016-04-14T19:39:35.000Z",
  "updated": "2016-04-14T19:39:35.000Z",
  "title": "Concordance of certain 3-braids and Gauss diagrams",
  "authors": [
    "Michael Brandenbursky"
  ],
  "comment": "8 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $\\beta:=\\sigma_1\\sigma_2^{-1}$ be a braid in $B_3$, where $B_3$ is the braid group on 3 strings and $\\sigma_1, \\sigma_2$ are the standard Artin generators. We use Gauss diagram formulas to show that for each natural number $n$ not divisible by $3$ the knot which is represented by the closure of the braid $\\beta^n$ is algebraically slice if and only if $n$ is odd. As a consequence, we deduce some properties of Lucas numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-14T19:39:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "concordance",
      "standard artin generators",
      "gauss diagram formulas",
      "braid group",
      "natural number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404273B"
    }
  }
}