{
  "id": "math/9912049",
  "version": "v1",
  "published": "1999-12-06T20:54:03.000Z",
  "updated": "1999-12-06T20:54:03.000Z",
  "title": "Immersed surfaces and Dehn surgery",
  "authors": [
    "Ying-Qing Wu"
  ],
  "comment": "29 pages, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $F$ be a proper essential immersed surface in a hyperbolic 3-manifold $M$ with boundary disjoint from a torus boundary component $T$ of $M$. Let $\\alpha$ be the set of coannular slopes of $F$ on $T$. The main theorem of the paper shows that there is a constant $K$ and a finite set of slopes $\\Lambda$ on $T$, such that if $\\beta$ is a slope on $T$ with $\\Delta(\\beta, \\alpha_i) > K$ for all $\\alpha_i$ in $\\alpha$, and $\\beta$ is not in $\\Lambda$, then $F$ remains incompressible after Dehn filling on $T$ along the slope $\\beta$. In certain sense, this means that $F$ survives most Dehn fillings. The proof uses minimal surface theory, integral of differential forms, and properties of geometrically finite groups. As a consequence of our method, it will also be shown that Freedman tubings of immersed geometrically finite surfaces are essential if the tubes are long enough.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-12-06T20:54:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10"
    ],
    "keywords": [
      "dehn surgery",
      "proper essential immersed surface",
      "torus boundary component",
      "minimal surface theory",
      "geometrically finite"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....12049W"
    }
  }
}