{
  "id": "0808.1795",
  "version": "v3",
  "published": "2008-08-13T17:35:02.000Z",
  "updated": "2011-05-31T15:07:36.000Z",
  "title": "A classification of smooth embeddings of 4-manifolds in 7-space, II",
  "authors": [
    "Diarmuid Crowley",
    "Arkadiy Skopenkov"
  ],
  "comment": "25 pages. Typos corrected and minor changes to improve exposition. To appear in the International Journal of Mathematics",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Let N be a closed, connected, smooth 4-manifold with H_1(N;Z)=0. Our main result is the following classification of the set E^7(N) of smooth embeddings N->R^7 up to smooth isotopy. Haefliger proved that the set E^7(S^4) with the connected sum operation is a group isomorphic to Z_{12}. This group acts on E^7(N) by embedded connected sum. Boechat and Haefliger constructed an invariant BH:E^7(N)->H_2(N;Z) which is injective on the orbit space of this action; they also described im(BH). We determine the orbits of the action: for u in im(BH) the number of elements in BH^{-1}(u) is GCD(u/2,12) if u is divisible by 2, or is GCD(u,3) if u is not divisible by 2. The proof is based on a new approach using modified surgery as developed by Kreck.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-05-31T15:07:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R40",
      "57R52",
      "57R65"
    ],
    "keywords": [
      "smooth embeddings",
      "classification",
      "main result",
      "smooth isotopy",
      "group acts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.1795C"
    }
  }
}