{
  "id": "1107.0240",
  "version": "v1",
  "published": "2011-07-01T14:47:21.000Z",
  "updated": "2011-07-01T14:47:21.000Z",
  "title": "On $L^p$ inequality for differential forms and $L^p$ cohomology of a semialgebraic set for $p>>1$",
  "authors": [
    "Leonid Shartser"
  ],
  "comment": "36 pages",
  "categories": [
    "math.GT",
    "math.AP",
    "math.DG"
  ],
  "abstract": "We study Poincar\\'e type $L^p$ inequality on a compact semialgebraic subset of $\\R^n$ for $p>>1$. First we derive a local inequality by using a Lipschitz deformation retraction with estimates on its derivatives. Then, we extend the local inequality to a global inequality by employing double complex technique. As a consequence we obtain an isomorphism between $L^p$ cohomology and singular cohomology of a normal compact semialgebraic pseudomanifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-01T14:47:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semialgebraic set",
      "differential forms",
      "local inequality",
      "normal compact semialgebraic pseudomanifold",
      "lipschitz deformation retraction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.0240S"
    }
  }
}