{
  "id": "1808.08605",
  "version": "v1",
  "published": "2018-08-26T18:18:38.000Z",
  "updated": "2018-08-26T18:18:38.000Z",
  "title": "On non-orientable surfaces in 4-manifolds",
  "authors": [
    "David Auckly",
    "Rustam Sadykov"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We find conditions under which a non-orientable closed surface S embedded into an orientable closed 4-manifold X can be represented by a connected sum of an embedded closed surface in X and an unknotted projective plane in a 4-sphere. This allows us to extend the Gabai 4-dimensional light bulb theorem and the Auckly-Kim-Melvin-Ruberman-Schwartz \"one is enough\" theorem to the case of non-orientable surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-26T18:18:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-orientable surfaces",
      "light bulb theorem",
      "embedded closed surface",
      "unknotted projective plane",
      "non-orientable closed surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}