{
  "id": "1206.0898",
  "version": "v2",
  "published": "2012-06-05T12:24:01.000Z",
  "updated": "2013-03-24T03:01:41.000Z",
  "title": "Bypasses for rectangular diagrams. Proof of Jones' conjecture and related questions",
  "authors": [
    "Ivan Dynnikov",
    "Maxim Prasolov"
  ],
  "comment": "50 pages, 62 Figures, numerous minor corrections",
  "journal": "Proc. of Moscow Math. Soc., V. 74 (2013), no. 1, p. 115-173",
  "categories": [
    "math.GT"
  ],
  "abstract": "In the present paper a criteria for a rectangular diagram to admit a simplification is given in terms of Legendrian knots. It is shown that there are two types of simplifications which are mutually independent in a sense. A new proof of the monotonic simplification theorem for the unknot is given. It is shown that a minimal rectangular diagram maximizes the Thurston--Bennequin number for the corresponding Legendrian links. Jones' conjecture about the invariance of the algebraic number of intersections of a minimal braid representing a fixed link type is proved.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-24T03:01:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "related questions",
      "conjecture",
      "minimal rectangular diagram maximizes",
      "monotonic simplification theorem",
      "minimal braid"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.0898D"
    }
  }
}