{
  "id": "1406.4496",
  "version": "v1",
  "published": "2014-06-17T19:45:53.000Z",
  "updated": "2014-06-17T19:45:53.000Z",
  "title": "An algorithm to classify rational 3-tangles",
  "authors": [
    "Bo-hyun Kwon"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "A $3$-$tangle$ $T$ is the disjoint union of $3$ properly embedded arcs in the unit 3-ball; it is called rational if there is a homeomorphism of pairs from $(B^3,T)$ to $(D^2\\times I,\\{x_1,x_2,x_3\\}\\times I)$. Two rational 3-tangles $T$ and $T'$ are isotopic if there is an orientation-preserving self-homeomorphism $h: (B^3, T)\\rightarrow (B^3,T')$ that is the identity map on the boundary. In this paper, we give an algorithm to check whether or not two rational 3-tangles are isotopic by using a modified version of Dehn's method for classifying simple closed curves on surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-17T19:45:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classify rational",
      "disjoint union",
      "classifying simple closed curves",
      "dehns method",
      "identity map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.4496K"
    }
  }
}