{
  "id": "1905.04089",
  "version": "v1",
  "published": "2019-05-10T11:51:54.000Z",
  "updated": "2019-05-10T11:51:54.000Z",
  "title": "Parity in Knotoids",
  "authors": [
    "Neslihan Gügümcü",
    "Louis Kauffman"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "This paper investigates the parity concept in knotoids in $S^2$ and in $\\mathbb{R}^2$ in relation with virtual knots. We show that the virtual closure map is not surjective and give specific examples of virtual knots that are not in the image. We introduce a planar version of the parity bracket polynomial for knotoids in $\\mathbb{R}^2$. By using the Nikonov/Manturov theorem on minimal diagrams of virtual knots we prove a conjecture of Turaev showing that minimal diagrams of knot-type knotoids have zero height.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-10T11:51:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M20"
    ],
    "keywords": [
      "virtual knots",
      "minimal diagrams",
      "virtual closure map",
      "parity bracket polynomial",
      "parity concept"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}