{
  "id": "2410.20307",
  "version": "v1",
  "published": "2024-10-27T02:12:04.000Z",
  "updated": "2024-10-27T02:12:04.000Z",
  "title": "An Excision Theorem in Heegaard Floer Theory",
  "authors": [
    "Neda Bagherifard"
  ],
  "comment": "35 pages, 16 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $Y_1$ be a closed, oriented 3-manifold and $\\Sigma$ denote a non-separating closed, orientable surface in $Y_1$ which consists of two connected components of the same genus. By cutting $Y_1$ along $\\Sigma$ and re-gluing it using an orientation-preserving diffeomorphism of $\\Sigma$ we obtain another closed, oriented 3-manifold $Y_2$. When the excision surface $\\Sigma$ is of genus one, we show that twisted Heegaard Floer homology groups of $Y_1$ and $Y_2$ (twisted with coefficients in the universal Novikov ring) are isomorphic. We use this excision theorem to demonstrate that certain manifolds are not related by the excision construction on a genus one surface. Additionally, we apply the excision formula to compute twisted Heegaard Floer homology groups of 0-surgery on certain two-component links, including some families of 2-bridge links.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-27T02:12:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "57K31",
      "57K18"
    ],
    "keywords": [
      "heegaard floer theory",
      "excision theorem",
      "twisted heegaard floer homology groups",
      "excision surface",
      "universal novikov"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}