{
  "id": "math/0505185",
  "version": "v2",
  "published": "2005-05-10T15:42:11.000Z",
  "updated": "2005-10-03T18:02:50.000Z",
  "title": "Generalized Seifert surfaces and signatures of colored links",
  "authors": [
    "David Cimasoni",
    "Vincent Florens"
  ],
  "comment": "40 pages, 20 figures",
  "journal": "Trans. Amer. Math. Soc. 360 (2008), 1223-1264",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we use `generalized Seifert surfaces' to extend the Levine-Tristram signature to colored links in S^3. This yields an integral valued function on the m-dimensional torus, where m is the number of colors of the link. The case m=1 corresponds to the Levine-Tristram signature. We show that many remarkable properties of the latter invariant extend to this m-variable generalization: it vanishes for achiral colored links, it is `piecewise continuous', and the places of the jumps are determined by the Alexander invariants of the colored link. Using a 4-dimensional interpretation and the Atiyah-Singer G-signature theorem, we also prove that this signature is invariant by colored concordance, and that it provides a lower bound for the `slice genus' of the colored link.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-10-03T18:02:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "generalized seifert surfaces",
      "levine-tristram signature",
      "atiyah-singer g-signature theorem",
      "alexander invariants",
      "slice genus"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5185C"
    }
  }
}