{
  "id": "2109.04085",
  "version": "v1",
  "published": "2021-09-09T08:04:51.000Z",
  "updated": "2021-09-09T08:04:51.000Z",
  "title": "$2$-complexes with unique embeddings in 3-space",
  "authors": [
    "Agelos Georgakopoulos",
    "Jaehoon Kim"
  ],
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove a 3-dimensional analogue: a simply-connected $2$-complex every link graph of which is 3-connected admits an essentially unique locally flat embedding into the 3-sphere, if it admits one at all. This can be thought of as a generalisation of the 3-dimensional Schoenflies theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-09T08:04:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unique embedding",
      "planar graph admits",
      "whitney states",
      "schoenflies theorem",
      "well-known theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}