{
  "id": "1007.3550",
  "version": "v2",
  "published": "2010-07-21T01:42:47.000Z",
  "updated": "2011-05-21T23:28:22.000Z",
  "title": "N-Degeneracy in rack homology and link invariants",
  "authors": [
    "Mohamed Elhamdadi",
    "Sam Nelson"
  ],
  "comment": "12 pages; revisions as requested by referee",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "The aim of this paper is to define a homology theory for racks with finite rank N and use it to define invariants of knots generalizing the CJKLS 2-cocycle invariants related to the invariants defined in [15]. For this purpose, we prove that N -degenerate chains form a sub-complex of the classical complex defining rack homology. If a rack has rack rank N = 1 then it is a quandle and our homology theory coincides with the CKJLS homology theory [6]. Nontrivial cocycles are used to define invariants of knots and examples of calculations for classical knots with up to 8 crossings and classical links with up to 7 crossings are provided.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-05-21T23:28:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25"
    ],
    "keywords": [
      "link invariants",
      "define invariants",
      "n-degeneracy",
      "classical complex defining rack homology",
      "degenerate chains form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.3550E"
    }
  }
}