{
  "id": "0706.1363",
  "version": "v1",
  "published": "2007-06-10T16:24:23.000Z",
  "updated": "2007-06-10T16:24:23.000Z",
  "title": "The rational homotopy type of a blow-up in the stable case",
  "authors": [
    "Pascal Lambrechts",
    "Don Stanley"
  ],
  "categories": [
    "math.AT",
    "math.SG"
  ],
  "abstract": "Suppose that f:V->W is an embedding of closed oriented manifolds whose normal bundle has the structure of a complex vector bundle. It is well known in both complex and symplectic geometry that one can then construct a manifold W' which is the blow-up of W along V. Assume that dim(W)>2.dim(V)+2 and that H^1(f) is injective. We construct an algebraic model of the rational homotopy type of the blow-up W' from an algebraic model of the embedding and the Chern classes of the normal bundle. This implies that if the space W is simply connected then the rational homotopy type of W' depends only on the rational homotopy class of f and on the Chern classes of the normal bundle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-10T16:24:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P62",
      "53D05"
    ],
    "keywords": [
      "rational homotopy type",
      "stable case",
      "normal bundle",
      "algebraic model",
      "rational homotopy class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.1363L"
    }
  }
}