{
  "id": "1609.09587",
  "version": "v1",
  "published": "2016-09-30T04:10:11.000Z",
  "updated": "2016-09-30T04:10:11.000Z",
  "title": "Constructions of invariants for surface-links via link invariants and applications to the Kauffman bracket",
  "authors": [
    "Sang Youl Lee"
  ],
  "comment": "35 pages, 15 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we formulate a construction of ideal coset invariants for surface-links in $4$-space using invariants for knots and links in $3$-space. We apply the construction to the Kauffman bracket polynomial invariant and obtain an invariant for surface-links called the Kauffman bracket ideal coset invariant of surface-links. We also define a series of new invariants $\\{{\\mathbf K}_{2n-1}(\\mathcal L) | n=2, 3, 4, \\ldots\\}$ for surface-links $\\mathcal L$ by using skein relations, which are more effective than the Kauffman bracket ideal coset invariant to distinguish given surface-links.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-30T04:10:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q45",
      "57M25"
    ],
    "keywords": [
      "kauffman bracket ideal coset invariant",
      "surface-links",
      "link invariants",
      "construction",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}