{
  "id": "2409.11961",
  "version": "v1",
  "published": "2024-09-18T13:12:13.000Z",
  "updated": "2024-09-18T13:12:13.000Z",
  "title": "On four-dimensional Dehn twists and Milnor fibrations",
  "authors": [
    "Hokuto Konno",
    "Jianfeng Lin",
    "Anubhav Mukherjee",
    "Juan Muñoz-Echániz"
  ],
  "comment": "72 pages. Comments are welcome!",
  "categories": [
    "math.GT",
    "math.AG",
    "math.DG",
    "math.SG"
  ],
  "abstract": "We study the monodromy diffeomorphism of Milnor fibrations of isolated complex surface singularities, by computing the family Seiberg--Witten invariant of Seifert-fibered Dehn twists using recent advances in monopole Floer homology. More precisely, we establish infinite order non-triviality results for boundary Dehn twists on indefinite symplectic fillings of links of minimally elliptic surface singularities. Using this, we exhibit a wide variety of new phenomena in dimension four: (1) smoothings of isolated complex surface singularities whose Milnor fibration has monodromy with infinite order as a diffeomorphism but with finite order as a homeomorphism, (2) robust Torelli symplectomorphisms that do not factor as products of Dehn--Seidel twists, (3) compactly supported exotic diffeomorphisms of exotic $\\mathbb{R}^4$'s and contractible manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-18T13:12:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K41",
      "57R58"
    ],
    "keywords": [
      "milnor fibration",
      "four-dimensional dehn twists",
      "isolated complex surface singularities",
      "establish infinite order non-triviality results",
      "robust torelli symplectomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 72,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}