{
  "id": "2205.13319",
  "version": "v1",
  "published": "2022-05-26T12:51:08.000Z",
  "updated": "2022-05-26T12:51:08.000Z",
  "title": "Protocorks and monopole Floer homology",
  "authors": [
    "Roberto Ladu"
  ],
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "We introduce and study a class of compact 4-manifolds with boundary that we call protocorks. Any exotic pair of simply connected closed 4-manifolds is related by a protocork twist, moreover, any cork is supported by a protocork. We prove a theorem on the relative Seiberg-Witten invariants of a protocork before and after twisting and a splitting theorem on the Floer homology of protocork boundaries. As a corollary we improve a theorem by Morgan and Szab\\'{o} regarding the variation of Seiberg-Witten invariants with an upper bound which depends only on the topology of the data. Moreover we show that for any cork, only the reduced Floer homology of its boundary contributes to the variation of the Seiberg-Witten invariants after a cork twist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-26T12:51:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monopole floer homology",
      "protocork twist",
      "reduced floer homology",
      "upper bound",
      "exotic pair"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}