{
  "id": "1210.6681",
  "version": "v2",
  "published": "2012-10-24T21:04:08.000Z",
  "updated": "2013-02-15T21:49:25.000Z",
  "title": "A graphical calculus for tangles in surfaces",
  "authors": [
    "Peter M. Johnson",
    "Sóstenes Lins"
  ],
  "comment": "Minor revision, terminology changes. 6 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show how the theory of tangles is equivalent to that of well-connected tangles. These are drawn on a surface with boundary, and equivalent via Reidemeister moves of a restricted kind. This reworking of the graphical foundations for link and tangle theory can be expected to have a variety of applications, including ones involving 3-manifolds. It opens the way to new approaches for defining `facial' state-sum invariants that depend in part on assigning substates to faces of tangle diagrams.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-15T21:49:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "graphical calculus",
      "equivalent",
      "reidemeister moves",
      "tangle theory",
      "state-sum invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.6681J"
    }
  }
}