{
  "id": "1703.07999",
  "version": "v1",
  "published": "2017-03-23T10:59:47.000Z",
  "updated": "2017-03-23T10:59:47.000Z",
  "title": "On codimension two embeddings up to link-homotopy",
  "authors": [
    "Benjamin Audoux",
    "Jean-Baptiste Meilhan",
    "Emmanuel Wagner"
  ],
  "comment": "13 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider knotted annuli in 4-space, called 2-string-links, which are knotted surfaces in codimension two that are naturally related, via closure operations, to both 2-links and 2-torus links. We classify 2-string-links up to link-homotopy by means of a 4-dimensional version of Milnor invariants. The key to our proof is that any 2-string link is link-homotopic to a ribbon one; this allows to use the homotopy classification obtained in the ribbon case by P. Bellingeri and the authors. Along the way, we give a Roseman-type result for immersed surfaces in 4-space. We also discuss the case of ribbon k-string links, for $k\\geq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-23T10:59:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "codimension",
      "link-homotopy",
      "embeddings",
      "closure operations",
      "milnor invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}