{
  "id": "1211.6830",
  "version": "v1",
  "published": "2012-11-29T07:30:21.000Z",
  "updated": "2012-11-29T07:30:21.000Z",
  "title": "Smoothings of singularities and symplectic surgery",
  "authors": [
    "Heesang Park",
    "András I. Stipsicz"
  ],
  "categories": [
    "math.GT",
    "math.AG",
    "math.SG"
  ],
  "abstract": "Suppose that $C=(C_1,..., C_m)$ is a configuration of 2-dimensional symplectic submanifolds in a symplectic 4-manifold $(X,\\omega)$ with connected, negative definite intersection graph $\\Gamma_C$. We show that by replacing an appropriate neighborhood of $\\cup C_i$ with a smoothing $W_S$ of a normal surface singularity $(S, 0)$ with resolution graph $\\Gamma_C$, the resulting 4-manifold admits a symplectic structure. This operation generalizes the rational blow-down operation of Fintushel-Stern for other configurations, and therefore extends Symington's result about symplectic rational blow-downs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-29T07:30:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R17",
      "14E15",
      "14J17"
    ],
    "keywords": [
      "symplectic surgery",
      "symplectic rational blow-downs",
      "extends symingtons result",
      "rational blow-down operation",
      "normal surface singularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.6830P"
    }
  }
}