{
  "id": "1407.3293",
  "version": "v2",
  "published": "2014-07-11T20:37:43.000Z",
  "updated": "2016-01-15T18:55:51.000Z",
  "title": "Comparing star surgery to rational blow-down",
  "authors": [
    "Laura Starkston"
  ],
  "comment": "v2 is a significant rewrite. The single example inequivalent to rational blow-down has been expanded to an infinite family. The sections on translating between monodromy substitutions and cap embeddings have been removed to be included separately as part of a more general treatment. Upgraded diffeomorphism classification to symplectic deformation + symplectomorphism",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We compare the star surgery operations introduced in [KS] to the generalized rational blow-down. We show that star surgery shares the properties that make rational blow-down useful for constructions of small exotic symplectic 4-manifolds. Then we show that star surgery operations provide a strictly more general class of operations by proving that there is an infinite family of star surgeries which are inequivalent to any sequence of generalized symplectic rational blow-downs. This answers a question posed to the author by Ozbagci. It also demonstrates that the monodromy substitutions coming from star surgery operations yield relations in planar mapping class monoids which cannot be positively generated by the relations determined in [EMVHM11] which come from the generalized rational blow-downs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-11T20:37:43.000Z",
      "title": "Examples and properties of star surgeries",
      "abstract": "Cut-and-paste operations on symplectic manifolds called star surgery were introduced and shown to be an effective tool in constructing examples of exotic 4-manifolds in [11]. Here we provide more examples of star surgery operations, and define an operation called sprouting which generates and infinite family of star surgeries from a single star surgery. Through these examples we begin to establish a broader correspondence between two different methods of finding and classifying symplectic fillings. We also prove that star surgeries always decrease Euler characteristic, and that there are examples of star surgeries which cannot be realized by a sequence of symplectic rational blow-downs.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-01-15T18:55:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "properties",
      "single star surgery",
      "symplectic rational blow-downs",
      "decrease euler characteristic",
      "star surgery operations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.3293S"
    }
  }
}