{
  "id": "1707.03279",
  "version": "v1",
  "published": "2017-07-11T14:05:24.000Z",
  "updated": "2017-07-11T14:05:24.000Z",
  "title": "A rank inequality for the annular Khovanov homology of 2-periodic links",
  "authors": [
    "Melissa Zhang"
  ],
  "comment": "42 pages, 32 figures",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "For a 2-periodic link $\\tilde L$ in the thickened annulus and its quotient link $L$, we exhibit a spectral sequence with $E^1 \\cong AKh(\\tilde L) \\otimes_{\\mathbb{F}_2} \\mathbb{F}_2[\\theta, \\theta^{-1}] \\rightrightarrows E^\\infty \\cong AKh(L) \\otimes_{\\mathbb{F}_2} \\mathbb{F}_2[\\theta, \\theta^{-1}].$ This spectral sequence splits along quantum and $sl_2$ weight space gradings, proving a rank inequality $rank\\ AKh^{j,k}(L) \\leq rank\\ AKh^{2j-k,k} (\\tilde L)$ for every pair of quantum and $sl_2$ weight space gradings $(j,k)$. We also present a few decategorified consequences and discuss partial results toward a similar statement for the Khovanov homology of 2-periodic links.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-11T14:05:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57M60"
    ],
    "keywords": [
      "annular khovanov homology",
      "rank inequality",
      "weight space gradings",
      "spectral sequence splits",
      "similar statement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}