{
  "id": "1812.11686",
  "version": "v1",
  "published": "2018-12-31T03:43:08.000Z",
  "updated": "2018-12-31T03:43:08.000Z",
  "title": "Computing closed essential surfaces in 3-manifolds",
  "authors": [
    "Benjamin A. Burton",
    "Stephan Tillmann"
  ],
  "comment": "25 pages, 15 figures; journal version of the conference paper arXiv:1212.1531",
  "categories": [
    "math.GT"
  ],
  "abstract": "We present a practical algorithm to test whether a 3-manifold given by a triangulation or an ideal triangulation contains a closed essential surface. This property has important theoretical and algorithmic consequences. As a testament to its practicality, we run the algorithm over a comprehensive body of closed 3-manifolds and knot exteriors, yielding results that were not previously known. The algorithm derives from the original Jaco-Oertel framework, involves both enumeration and optimisation procedures, and combines several techniques from normal surface theory. Our methods are relevant for other difficult computational problems in 3-manifold theory, such as the recognition problem for knots, links and 3-manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-31T03:43:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57N10"
    ],
    "keywords": [
      "computing closed essential surfaces",
      "ideal triangulation contains",
      "normal surface theory",
      "original jaco-oertel framework",
      "knot exteriors"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}