{
  "id": "1702.06692",
  "version": "v1",
  "published": "2017-02-22T07:25:44.000Z",
  "updated": "2017-02-22T07:25:44.000Z",
  "title": "Surgery formulae for the Seiberg-Witten invariant of plumbed 3-manifolds",
  "authors": [
    "Tamás László",
    "János Nagy",
    "András Némethi"
  ],
  "comment": "24 pages",
  "categories": [
    "math.GT",
    "math.AG"
  ],
  "abstract": "Assume that $M(\\mathcal{T})$ is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph $\\mathcal{T}$. We consider the combinatorial multivariable Poincar\\'e series associated with $\\mathcal{T}$ and its counting functions, which encode rich topological information. Using the `periodic constant' of the series (with reduced variables) we prove surgery formulae for the normalized Seiberg-Witten invariants: the periodic constant appears as the difference of the Seiberg-Witten invariants associated with $M(\\mathcal{T})$ and $M(\\mathcal{T}\\setminus\\mathcal{I})$, where $\\mathcal{I}$ is an arbitrary subset of the set of vertices of $\\mathcal{T}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-22T07:25:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "seiberg-witten invariant",
      "surgery formulae",
      "rational homology sphere",
      "periodic constant appears",
      "encode rich topological information"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}