{
  "id": "2405.04737",
  "version": "v2",
  "published": "2024-05-08T00:56:52.000Z",
  "updated": "2024-06-06T02:05:45.000Z",
  "title": "Non-orientable 4-genus of torus knots",
  "authors": [
    "Megan Fairchild",
    "Hailey Jay Garcia",
    "Jake Murphy",
    "Hannah Percle"
  ],
  "comment": "13 pages, 2 figures, corrected typo in references, added attribution to Lobb for disproving non-orientable analog of Milnor conjecture",
  "categories": [
    "math.GT"
  ],
  "abstract": "The non-orientable 4-genus of a knot $K$ in $S^{3}$, denoted $\\gamma_4(K)$, measures the minimum genus of a non-orientable surface in $B^{4}$ bounded by $K$. We compute bounds for the non-orientable 4-genus of knots $T_{5, q}$ and $T_{6, q}$, extending previous research. Additionally, we provide a generalized, non-recursive formula for $d(S^{3}_{-1}(T_{p,q}))$, the $d$-invariant of -1-surgery on torus knots.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-06-06T02:05:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57M25"
    ],
    "keywords": [
      "torus knots",
      "minimum genus",
      "non-orientable surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}