{
  "id": "math/0701208",
  "version": "v1",
  "published": "2007-01-07T15:03:40.000Z",
  "updated": "2007-01-07T15:03:40.000Z",
  "title": "Complementary regions for immersions of surfaces",
  "authors": [
    "Tahl Nowik"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "Let F be a closed surface and i:F \\to S^3 a generic immersions. Then S^3 - i(F) is a union of connected regions, which may be separated into two sets {U_j} and {V_j} by a checkerboard coloring. For k \\geq 0, let a_k, b_k be the number of components U_j, V_j with \\chi(U_j) = 1-k, \\chi(V_j)=1-k, respectively. Two more integers attached to i are the number N of triple points of i, and \\chi=\\chi(F). In this work we determine what sets of data ({a_k}, {b_k}, \\chi, N) may appear in this way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-07T15:03:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complementary regions",
      "generic immersions",
      "triple points",
      "connected regions",
      "closed surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1208N"
    }
  }
}