{
  "id": "math/0509621",
  "version": "v2",
  "published": "2005-09-27T07:42:45.000Z",
  "updated": "2007-12-11T12:02:01.000Z",
  "title": "A new invariant and parametric connected sum of embeddings",
  "authors": [
    "A. Skopenkov"
  ],
  "comment": "13 pages, to appear in Fundamenta Mathematicae",
  "journal": "Fund. Math. 197 (2007), 253--269",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "We define an isotopy invariant of embeddings N -> R^m of manifolds into Euclidean space. This invariant together with the \\alpha-invariant of Haefliger-Wu is complete in the dimension range where the \\alpha-invariant could be incomplete. We also define parametric connected sum of certain embeddings (analogous to surgery). This allows to obtain new completeness results for the \\alpha-invariant and the following estimation of isotopy classes of embeddings. For the piecewise-linear category, a (3n-2m+2)-connected n-manifold N and (4n+4)/3 < m < (3n+3)/2 each preimage of \\alpha-invariant injects into a quotient of H_{3n-2m+3}(N), where the coefficients are Z for m-n odd and Z_2 for m-n even.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-12-11T12:02:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "embeddings",
      "define parametric connected sum",
      "isotopy invariant",
      "m-n odd",
      "euclidean space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9621S"
    }
  }
}