{
  "id": "2501.12673",
  "version": "v1",
  "published": "2025-01-22T06:16:27.000Z",
  "updated": "2025-01-22T06:16:27.000Z",
  "title": "Exotic families of embeddings",
  "authors": [
    "Dave Auckly",
    "Daniel Ruberman"
  ],
  "comment": "25 page, 9 figures",
  "journal": "Frontiers in geometry and topology, Proc. Sympos. Pure Math., 109, 71--98, (2024) Amer. Math. Soc., Providence, RI",
  "categories": [
    "math.GT"
  ],
  "abstract": "We construct a number of topologically trivial but smoothly non-trivial families of embeddings of 3-manifolds in 4-manifolds. These include embeddings of homology spheres in $S^4$ that are not isotopic but have diffeomorphic complements, and families (parameterized by high-dimensional spheres) of embeddings of any 3-manifold that embeds in a blown-up K3 surface. In each case, the families are constructed so as to be topologically trivial in an appropriate sense. We also illustrate a general technique for converting a non-trivial family of embeddings into a non-trivial family of submanifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-22T06:16:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K41",
      "57N37"
    ],
    "keywords": [
      "embeddings",
      "exotic families",
      "non-trivial family",
      "topologically trivial",
      "blown-up k3 surface"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}