{
  "id": "2006.14525",
  "version": "v1",
  "published": "2020-06-25T16:22:07.000Z",
  "updated": "2020-06-25T16:22:07.000Z",
  "title": "Conjugation Curvature in Solvable Baumslag-Solitar Groups",
  "authors": [
    "Jennifer Taback",
    "Alden Walker"
  ],
  "comment": "50 pages, 3 figures",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "For an element in $BS(1,n) = \\langle t,a | tat^{-1} = a^n \\rangle$ written in the normal form $t^{-u}a^vt^w$ with $u,w \\geq 0$ and $v \\in \\mathbb{Z}$, we exhibit a geodesic word representing the element and give a formula for its word length with respect to the generating set $\\{t,a\\}$. Using this word length formula, we prove that there are sets of elements of positive density of positive, negative and zero conjugation curvature, as defined by Bar Natan, Duchin and Kropholler.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-25T16:22:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F10"
    ],
    "keywords": [
      "solvable baumslag-solitar groups",
      "zero conjugation curvature",
      "word length formula",
      "bar natan",
      "normal form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}