{
  "id": "1101.1412",
  "version": "v2",
  "published": "2011-01-07T11:53:20.000Z",
  "updated": "2011-07-14T15:43:51.000Z",
  "title": "Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial",
  "authors": [
    "Jessica E. Banks"
  ],
  "comment": "37 pages, 28 figures; v2 Main results generalised from alternating links to homogeneous links. Title changed",
  "doi": "10.1007/s10711-012-9786-1",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give a geometric proof of the following result of Juhasz. \\emph{Let $a_g$ be the leading coefficient of the Alexander polynomial of an alternating knot $K$. If $|a_g|<4$ then $K$ has a unique minimal genus Seifert surface.} In doing so, we are able to generalise the result, replacing `minimal genus' with `incompressible' and `alternating' with `homogeneous'. We also examine the implications of our proof for alternating links in general.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-14T15:43:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57M15"
    ],
    "keywords": [
      "reduced alexander polynomial",
      "homogeneous links",
      "unique minimal genus seifert surface",
      "geometric proof"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1412B"
    }
  }
}