{
  "id": "1401.5336",
  "version": "v3",
  "published": "2014-01-21T14:59:27.000Z",
  "updated": "2016-02-21T13:33:09.000Z",
  "title": "Signature, positive Hopf plumbing and the Coxeter transformation",
  "authors": [
    "Livio Liechti"
  ],
  "comment": "16 pages, 5 figures, with appendix by Peter Feller and Livio Liechti",
  "journal": "Osaka J. Math. 53 (2016), 251-266",
  "categories": [
    "math.GT"
  ],
  "abstract": "By a theorem of A'Campo, the eigenvalues of certain Coxeter transformations are positive real or lie on the unit circle. By optimally bounding the signature of tree-like positive Hopf plumbings from below by the genus, we prove that at least two thirds of them lie on the unit circle. In contrast, we show that for divide links, the signature cannot be linearly bounded from below by the genus.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-08T15:12:48.000Z",
      "comment": "15 pages, 5 figures, with an appendix by Peter Feller and Livio Liechti",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-02-21T13:33:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "coxeter transformation",
      "unit circle",
      "divide links",
      "tree-like positive hopf plumbings",
      "eigenvalues"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.5336L"
    }
  }
}