{
  "id": "1909.09245",
  "version": "v1",
  "published": "2019-09-19T22:01:30.000Z",
  "updated": "2019-09-19T22:01:30.000Z",
  "title": "Annular Rasmussen invariants: Properties and 3-braid classification",
  "authors": [
    "Gage Martin"
  ],
  "comment": "33 pages, 26 figures",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "We prove that for a fixed braid index there are only finitely many possible shapes of the annular Rasmussen $d_t$ invariant of braid closures. Applying the same perspective to the knot Floer invariant $\\Upsilon_K(t)$, we show that for a fixed concordance genus of $K$ there are only finitely many possibilities for $\\Upsilon_K(t)$. Focusing on the case of 3-braids, we compute the Rasmussen $s$ invariant and the annular Rasmussen $d_t$ invariant of all 3-braid closures. As a corollary, we show that the vanishing/non-vanishing of the $\\psi$ invariant is entirely determined by the $s$ invariant and the self-linking number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-19T22:01:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "20F36",
      "81R50",
      "57Q60",
      "57M25"
    ],
    "keywords": [
      "annular rasmussen invariants",
      "properties",
      "classification",
      "knot floer invariant",
      "fixed concordance genus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}