{
  "id": "2408.02857",
  "version": "v1",
  "published": "2024-08-05T22:53:51.000Z",
  "updated": "2024-08-05T22:53:51.000Z",
  "title": "Correction terms of double branched covers and symmetries of immersed curves",
  "authors": [
    "Jonathan Hanselman",
    "Marco Marengon",
    "Biji Wong"
  ],
  "comment": "61 pages, 22 figures, 2 tables. Comments welcome",
  "categories": [
    "math.GT"
  ],
  "abstract": "We use the immersed curves description of bordered Floer homology to study $d$-invariants of double branched covers $\\Sigma_2(L)$ of arborescent links $L \\subset S^3$. We define a new invariant $\\Delta_{sym}$ of bordered $\\mathbb{Z}_2$-homology solid tori from an involution of the associated immersed curves and relate it to both the $d$-invariants and the Neumann-Siebenmann $\\bar\\mu$-invariants of certain fillings. We deduce that if $L$ is a 2-component arborescent link and $\\Sigma_2(L)$ is an L-space, then the spin $d$-invariants of $\\Sigma_2(L)$ are determined by the signatures of $L$. By a separate argument, we show that the same relationship holds when $L$ is a 2-component link that admits a certain symmetry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-05T22:53:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M12",
      "57M25",
      "57R58"
    ],
    "keywords": [
      "double branched covers",
      "correction terms",
      "arborescent link",
      "homology solid tori",
      "bordered floer homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}