{
  "id": "1612.05953",
  "version": "v1",
  "published": "2016-12-18T17:21:04.000Z",
  "updated": "2016-12-18T17:21:04.000Z",
  "title": "Annular Khovanov-Lee homology, braids, and cobordisms",
  "authors": [
    "J. Elisenda Grigsby",
    "Anthony M. Licata",
    "Stephan M. Wehrli"
  ],
  "comment": "33 pages, 2 figures",
  "categories": [
    "math.GT",
    "math.QA",
    "math.RT"
  ],
  "abstract": "We prove that the Khovanov-Lee complex of an oriented link, L, in a thickened annulus, A x I, has the structure of a bifiltered complex whose filtered chain homotopy type is an invariant of the isotopy class of L in A x I. Using ideas of Ozsvath-Stipsicz-Szabo as reinterpreted by Livingston, we use this structure to define a family of annular Rasmussen invariants that yield information about annular and non-annular cobordisms. Focusing on the special case of annular links obtained as braid closures, we use the behavior of the annular Rasmussen invariants to obtain a necessary condition for braid quasipositivity and a sufficient condition for right-veeringness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-18T17:21:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "20F36",
      "81R50",
      "57Q60"
    ],
    "keywords": [
      "annular khovanov-lee homology",
      "annular rasmussen invariants",
      "filtered chain homotopy type",
      "sufficient condition",
      "yield information"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}