{
  "id": "1208.0524",
  "version": "v1",
  "published": "2012-08-02T15:55:47.000Z",
  "updated": "2012-08-02T15:55:47.000Z",
  "title": "Macroscopic dimension and duality groups",
  "authors": [
    "Alexander Dranishnikov"
  ],
  "comment": "This is a short English version of a paper published in Russian",
  "categories": [
    "math.GT",
    "math.AT",
    "math.DG"
  ],
  "abstract": "We show that for a rationally inessential orientable closed $n$-manifold $M$ whose fundamental group $\\pi$ is a duality group the macroscopic dimension of its universal cover is strictly less than $n$:$$ \\dim_{MC}\\Wi M<n.$$ As a corollary we obtain the following 0.1 Theorem. The inequality $ \\dim_{MC}\\Wi M<n$ holds for the universal cover of a closed spin $n$-manifold $M$ with a positive scalar curvature metric if the fundamental group $\\pi_1(M)$ is a virtual duality group virtually satisfying the Analytic Novikov Conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-02T15:55:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23"
    ],
    "keywords": [
      "macroscopic dimension",
      "fundamental group",
      "universal cover",
      "analytic novikov conjecture",
      "positive scalar curvature metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.0524D"
    }
  }
}