{
  "id": "2407.06923",
  "version": "v1",
  "published": "2024-07-09T14:58:05.000Z",
  "updated": "2024-07-09T14:58:05.000Z",
  "title": "On fundamental groups of spaces of (framed) embeddings of the circle in a $4$-manifold",
  "authors": [
    "Danica Kosanovicć"
  ],
  "comment": "21 pages, 1 figure",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Motivated by recent results on diffeomorphisms, this paper investigates fundamental groups of spaces of embeddings of $S^1$ and $S^1\\times D^3$ in 4-manifolds. We express the latter (framed) case in terms of the former, and study examples of the form $M\\# S^1\\times S^3$ in detail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-09T14:58:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R40",
      "57K40",
      "57K45",
      "58D10"
    ],
    "keywords": [
      "fundamental groups",
      "embeddings",
      "study examples",
      "diffeomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}