{
  "id": "1701.07170",
  "version": "v1",
  "published": "2017-01-25T05:46:11.000Z",
  "updated": "2017-01-25T05:46:11.000Z",
  "title": "Yoshikawa Moves on Marked Graphs via Roseman's Theorem",
  "authors": [
    "Oleg Chterental"
  ],
  "comment": "28 pages, 29 figures. Comments are welcome",
  "categories": [
    "math.GT"
  ],
  "abstract": "Yoshikawa [Yo] conjectured that a certain set of moves on marked graph diagrams generates the isotopy relation for surface links in ${\\mathbb R}^4$, and this was proved by Swenton [S] and Kearton-Kurlin [KK]. In this paper, we find another proof of this fact for the case of 2-links (surface links with spherical components). The proof involves a version of Roseman's theorem [R] for branch-point-free broken surface diagrams of 2-links and a construction of marked graphs from branch-point-free broken surface diagrams. As an application, we find that Brunnian 2-links are ribbon.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-25T05:46:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rosemans theorem",
      "yoshikawa moves",
      "branch-point-free broken surface diagrams",
      "surface links",
      "marked graph diagrams generates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}