{
  "id": "2501.08750",
  "version": "v1",
  "published": "2025-01-15T12:09:19.000Z",
  "updated": "2025-01-15T12:09:19.000Z",
  "title": "On $h$-cobordisms of complexity $2$",
  "authors": [
    "Roberto Ladu"
  ],
  "comment": "29 pages, 19 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study $5$-dimensional $h$-cobordisms of Morgan-Szab\\'o complexity $2$. We compute the monopole Floer homology and the action of the twisting involution of the protocork boundary associated with such $h$-cobordisms, obtaining an obstruction for $h$-cobordisms between exotic pairs to have minimal complexity. We construct the first examples of $h$-cobordisms of non-minimal, in fact, arbitrarily large, complexity between an exotic pair of closed, $1$-connected $4$-manifolds. Further applications include strong corks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-15T12:09:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R80",
      "57R58",
      "57R55",
      "57K41"
    ],
    "keywords": [
      "cobordisms",
      "exotic pair",
      "monopole floer homology",
      "protocork boundary",
      "morgan-szabo complexity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}