{
  "id": "1701.04924",
  "version": "v1",
  "published": "2017-01-18T02:08:57.000Z",
  "updated": "2017-01-18T02:08:57.000Z",
  "title": "Search for torsion in Khovanov homology",
  "authors": [
    "Sujoy Mukherjee",
    "Józef H. Przytycki",
    "Marithania Silvero",
    "Xiao Wang",
    "Seung Yeop Yang"
  ],
  "comment": "33 pages, 8 figures, and 33 tables",
  "categories": [
    "math.GT"
  ],
  "abstract": "In the Khovanov homology of links, presence of $\\mathbb{Z}_2$-torsion is a very common phenomenon. Finite number of examples of knots with $\\mathbb{Z}_n$-torsion for $n>2$ were also known, none for $n>8$. In this paper, we prove that there are infinite families of links whose Khovanov homology contains $\\mathbb{Z}_n$-torsion for $2 < n < 9$ and $\\mathbb{Z}_{2^s}$-torsion for $s < 24$. We also introduce $4$-braid links with $\\mathbb{Z}_3$-torsion which are counterexamples to the PS braid conjecture. We also provide an infinite family of knots with $\\mathbb{Z}_5$-torsion in reduced Khovanov homology and $\\mathbb{Z}_3$-torsion in odd Khovanov homology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-18T02:08:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "ps braid conjecture",
      "odd khovanov homology",
      "khovanov homology contains",
      "common phenomenon",
      "finite number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}