{
  "id": "1611.01178",
  "version": "v1",
  "published": "2016-11-03T20:22:42.000Z",
  "updated": "2016-11-03T20:22:42.000Z",
  "title": "Equivalence of two definitions of set-theoretic Yang-Baxter homology",
  "authors": [
    "Jozef H. Przytycki",
    "Xiao Wang"
  ],
  "comment": "15 pages, 12 pictures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In 2004, Carter, Elhamdadi and Saito defined a homology theory for set-theoretic Yang-Baxter operators(we will call it the \"algebraic\" version in this article). In 2012, Przytycki defined another homology theory for pre-Yang-Baxter operators which has a nice graphic visualization(we will call it the \"graphic\" version in this article). We show that they are equivalent. The \"graphic\" homology is also defined for pre-Yang-Baxter operators, and we give some examples of it's one-term and two-term homologies. In the two-term case, we have found torsion in homology of Yang-Baxter operator that yields the Jones polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-03T20:22:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "18G60"
    ],
    "keywords": [
      "set-theoretic yang-baxter homology",
      "equivalence",
      "homology theory",
      "pre-yang-baxter operators",
      "definitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}