{
  "id": "math/0401035",
  "version": "v5",
  "published": "2004-01-05T20:22:25.000Z",
  "updated": "2005-07-10T16:19:32.000Z",
  "title": "Minimal surface representations of virtual knots and links",
  "authors": [
    "H. A. Dye",
    "Louis H. Kauffman"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-22.abs.html Version 5: a minor correction and a citation added",
  "journal": "Algebr. Geom. Topol. 5 (2005) 509-535",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "Kuperberg [Algebr. Geom. Topol. 3 (2003) 587-591] has shown that a virtual knot corresponds (up to generalized Reidemeister moves) to a unique embedding in a thichened surface of minimal genus. If a virtual knot diagram is equivalent to a classical knot diagram then this minimal surface is a sphere. Using this result and a generalised bracket polynomial, we develop methods that may determine whether a virtual knot diagram is non-classical (and hence non-trivial). As examples we show that, except for special cases, link diagrams with a single virtualization and link diagrams with a single virtual crossing are non-classical.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2005-07-10T16:19:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57N05"
    ],
    "keywords": [
      "minimal surface representations",
      "virtual knot diagram",
      "link diagrams",
      "virtual knot corresponds",
      "generalised bracket polynomial"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1035D"
    }
  }
}