{
  "id": "math/0610741",
  "version": "v1",
  "published": "2006-10-25T03:16:07.000Z",
  "updated": "2006-10-25T03:16:07.000Z",
  "title": "3-manifolds and 4-dimensional surgery",
  "authors": [
    "Masayuki Yamasaki"
  ],
  "comment": "AMS-LaTeX, 4 pages, no figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $X$ be a connected compact 3-manifold with non-empty boundary. Consider the boundary $M$ of $X\\times D^2$. $M$ is a 4-dimensional closed manifold and has the same fundamental group as $X$. Various examples of $X$ are known for which a certain assembly map $A:H_4(X;L)\\to L_4(\\pi_1(X))$ is injective. For such an $X$ and any CW-spine $B$ of $X$, there is a $UV^1$-map $p:M\\to B$. For any $\\epsilon>0$, if the surgery obstruction for a TOP normal map $(f,b):N\\to M$ vanishes, we can perform surgery on $f$ to change it into a $p^{-1}(\\epsilon)$-controlled homotopy equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-25T03:16:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R67"
    ],
    "keywords": [
      "non-empty boundary",
      "fundamental group",
      "surgery obstruction",
      "normal map",
      "perform surgery"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10741Y"
    }
  }
}