{
  "id": "1411.1621",
  "version": "v1",
  "published": "2014-11-06T14:09:17.000Z",
  "updated": "2014-11-06T14:09:17.000Z",
  "title": "Casson towers and slice links",
  "authors": [
    "Jae Choon Cha",
    "Mark Powell"
  ],
  "comment": "34 pages, 17 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that a Casson tower of height 4 contains a flat embedded disc bounded by the attaching circle. We also prove disc embedding results for height 2 and 3 Casson towers which are embedded into a 4-manifold, with some additional fundamental group assumptions. In the proof we create a capped grope from a Casson tower and use a refined height raising argument to establish the existence of a symmetric grope of height 4 which has two layers of caps, data which is sufficient for a topological disc with the desired boundary to exist. As applications, we present new slice knots and links by giving direct geometric constructions of slicing discs. In particular we construct a family of slice knots which are potential counterexamples to the homotopy ribbon slice conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-06T14:09:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N13",
      "57N70",
      "57M25"
    ],
    "keywords": [
      "casson tower",
      "slice links",
      "homotopy ribbon slice conjecture",
      "slice knots",
      "additional fundamental group assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1621C"
    }
  }
}