{
  "id": "math/0407347",
  "version": "v2",
  "published": "2004-07-21T17:52:10.000Z",
  "updated": "2005-11-06T13:17:24.000Z",
  "title": "Contact homology and one parameter families of Legendrian knots",
  "authors": [
    "Tamas Kalman"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper46.abs.html",
  "journal": "Geom. Topol. 9(2005) 2013-2078",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We consider S^1-families of Legendrian knots in the standard contact R^3. We define the monodromy of such a loop, which is an automorphism of the Chekanov-Eliashberg contact homology of the starting (and ending) point. We prove this monodromy is a homotopy invariant of the loop. We also establish techniques to address the issue of Reidemeister moves of Lagrangian projections of Legendrian links. As an application, we exhibit a loop of right-handed Legendrian torus knots which is non-contractible in the space Leg(S^1,R^3) of Legendrian knots, although it is contractible in the space Emb(S^1,R^3) of smooth knots. For this result, we also compute the contact homology of what we call the Legendrian closure of a positive braid and construct an augmentation for each such link diagram.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-11-06T13:17:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D40",
      "57M25"
    ],
    "keywords": [
      "legendrian knots",
      "parameter families",
      "chekanov-eliashberg contact homology",
      "right-handed legendrian torus knots",
      "reidemeister moves"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7347K"
    }
  }
}