{
  "id": "1405.4061",
  "version": "v3",
  "published": "2014-05-16T03:58:08.000Z",
  "updated": "2014-12-22T07:43:06.000Z",
  "title": "Characterization of positive links and the $s$-invariant for links",
  "authors": [
    "Tetsuya Abe",
    "Keiji Tagami"
  ],
  "comment": "28 pages, 17 figures, the statements of Corollary 1.7 and Corollary 7.4 were corrected, Question 10.5 and two references were added",
  "categories": [
    "math.GT"
  ],
  "abstract": "We characterize positive links in terms of strong quasipositivity, homogeneity and the value of Rasmussen, Beliakova and Wehrli's $s$-invariant. We also study almost positive links, in particular, determine the $s$-invariants of almost positive links. This result suggests that all almost positive links might be strongly quasipositive. On the other hand, it implies that almost positive links are never homogeneous links.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-13T05:47:51.000Z",
      "comment": "28 pages, 17 figures, the statement of Corollary 7.4 was corrected, Question 10.5 and two references were added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-12-22T07:43:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characterization",
      "strong quasipositivity",
      "homogeneous links",
      "characterize positive links",
      "homogeneity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.4061A"
    }
  }
}