{
  "id": "1805.01094",
  "version": "v1",
  "published": "2018-05-03T03:15:22.000Z",
  "updated": "2018-05-03T03:15:22.000Z",
  "title": "Distortion of surfaces in $3$--manifolds",
  "authors": [
    "Hoang Thanh Nguyen"
  ],
  "comment": "26 pages, 1 figure",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let $g \\colon S \\looparrowright N$ be a properly immersed $\\pi_1$--injective surface in a non-geometric $3$--manifold $N$. We compute the distortion of $\\pi_1(S)$ in $\\pi_1(N)$. The only possibility of the distortion is linear, quadratic, exponential, and double exponential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-03T03:15:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "20F65",
      "20F67"
    ],
    "keywords": [
      "distortion",
      "injective surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}