{
  "id": "1712.05719",
  "version": "v1",
  "published": "2017-12-15T15:50:07.000Z",
  "updated": "2017-12-15T15:50:07.000Z",
  "title": "Winding number $m$ and $-m$ patterns acting on concordance",
  "authors": [
    "Allison N. Miller"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that for any winding number $m>0$ pattern $P$ and winding number $-m$ pattern $Q$, there exist knots $K$ such that the minimal genus of a cobordism between $P(K)$ and $Q(K)$ is arbitrarily large. This answers a question posed by Cochran-Harvey [CH17] and generalizes a result of Kim-Livingston [KL05].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-15T15:50:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "winding number",
      "patterns acting",
      "concordance",
      "minimal genus",
      "arbitrarily large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}