{
  "id": "1006.5707",
  "version": "v6",
  "published": "2010-06-29T19:25:22.000Z",
  "updated": "2013-01-24T17:46:14.000Z",
  "title": "Smooth structures on pseudomanifolds with isolated conical singularities",
  "authors": [
    "Hong Van Le",
    "Petr Somberg",
    "Jiri Vanzura"
  ],
  "comment": "26 pages, final version",
  "journal": "Acta Math Vietnam (2013) 38:33-54",
  "doi": "10.1007/s40306-013-0009-0",
  "categories": [
    "math.DG",
    "math.SG"
  ],
  "abstract": "In this note we introduce the notion of a smooth structure on a conical pseudomanifold $M$ in terms of $C^\\infty$-rings of smooth functions on $M$. For a finitely generated smooth structure $C^\\infty (M)$ we introduce the notion of the Nash tangent bundle, the Zariski tangent bundle, the tangent bundle of $M$, and the notion of characteristic classes of $M$. We prove the vanishing of a Nash vector field at a singular point for a special class of Euclidean smooth structures on $M$. We introduce the notion of a conical symplectic form on $M$ and show that it is smooth with respect to a Euclidean smooth structure on $M$. If a conical symplectic structure is also smooth with respect to a compatible Poisson smooth structure $C^\\infty (M)$, we show that its Brylinski-Poisson homology groups coincide with the de Rham homology groups of $M$. We show nontrivial examples of these smooth conical symplectic-Poisson pseudomanifolds.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2013-01-24T17:46:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51H25",
      "53D05",
      "53D17"
    ],
    "keywords": [
      "isolated conical singularities",
      "euclidean smooth structure",
      "brylinski-poisson homology groups coincide",
      "zariski tangent bundle",
      "rham homology groups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.5707V"
    }
  }
}