{
  "id": "1810.09649",
  "version": "v1",
  "published": "2018-10-23T04:12:28.000Z",
  "updated": "2018-10-23T04:12:28.000Z",
  "title": "$\\partial$-reducible handle additions",
  "authors": [
    "Han Lou",
    "Mingxing Zhang"
  ],
  "comment": "10 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $M$ be a simple 3-manifold, and $F$ be a component of $\\partial M$ of genus at least 2. Let $\\alpha$ and $\\beta$ be separating slopes on $F$. Let $M(\\alpha)$ (resp.$M(\\beta)$) be the manifold obtained by adding a 2-handle along $\\alpha$ (resp.$\\beta$). If $M(\\alpha)$ and $M(\\beta)$ are $\\partial$-reducible, then the distance (intersection number) between $\\alpha$ and $\\beta$ is at most 8.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-23T04:12:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "reducible handle additions",
      "intersection number",
      "separating slopes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}