{
  "id": "2310.15748",
  "version": "v1",
  "published": "2023-10-24T11:47:39.000Z",
  "updated": "2023-10-24T11:47:39.000Z",
  "title": "On the complement to a real caustic germ of type $E_6$",
  "authors": [
    "Vyacheslav D. Sedykh"
  ],
  "comment": "59 pages, 21 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove that the complement to the caustic of a stable Lagrangian map germ of type $E_6^\\pm$ has seven connected components, six of which are contractible and one is homotopy equivalent to a circle. The inverse image of the noncontractible component under this map has three connected components. The restriction of the map to one of them is a two-sheeted covering; the restriction to each of the other two is a diffeomorphism. The table of adjacency indexes of type $E_6^\\pm$ monosingularity to multisingularities of a generic Lagrangian map is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-24T11:47:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P25",
      "58K15",
      "14Q30",
      "53D12",
      "57R45",
      "58K35",
      "58K60"
    ],
    "keywords": [
      "real caustic germ",
      "complement",
      "stable lagrangian map germ",
      "generic lagrangian map",
      "seven connected components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}