{
  "id": "math/0410047",
  "version": "v1",
  "published": "2004-10-04T08:24:27.000Z",
  "updated": "2004-10-04T08:24:27.000Z",
  "title": "Embedded spheres in S^2\\times S^1#...#S^2\\times S^1",
  "authors": [
    "Siddhartha Gadgil"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We give an algorithm to decide which elements of pi_2(S^2\\times S^1#...#S^2\\times S^1) can be represented by embedded spheres. Such spheres correspond to splittings of the free group on k generators. Equivalently our algorithm decides whether, for a handlebody N, an element in pi_2(N,\\partial N) can be represented by an embedded disc. We also give an algorithm to decide when classes in $\\pi_2(S^2\\times S^1#...#S^2\\times S^1)$ can be represented by disjoint embedded spheres. We introduce the splitting complex of a free group which is analogous to the complex of curves of a surface. We show that the splitting complex of the free group on k generators embeds in the complex of curves of a surface of genus $k$ as a quasi-convex subset.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-04T08:24:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M05",
      "57M07",
      "20E06"
    ],
    "keywords": [
      "free group",
      "splitting complex",
      "quasi-convex subset",
      "disjoint embedded spheres",
      "spheres correspond"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10047G"
    }
  }
}