{
  "id": "1104.5690",
  "version": "v1",
  "published": "2011-04-29T18:06:07.000Z",
  "updated": "2011-04-29T18:06:07.000Z",
  "title": "Twisted conjugacy in braid groups",
  "authors": [
    "Juan González-Meneses",
    "Enric Ventura"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this note we solve the twisted conjugacy problem for braid groups, i.e. we propose an algorithm which, given two braids $u,v\\in B_n$ and an automorphism $\\phi \\in Aut (B_n)$, decides whether $v=(\\phi (x))^{-1}ux$ for some $x\\in B_n$. As a corollary, we deduce that each group of the form $B_n \\rtimes H$, a semidirect product of the braid group $B_n$ by a torsion-free hyperbolic group $H$, has solvable conjugacy problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-29T18:06:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F10"
    ],
    "keywords": [
      "braid group",
      "torsion-free hyperbolic group",
      "solvable conjugacy problem",
      "semidirect product",
      "twisted conjugacy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.5690G"
    }
  }
}