{
  "id": "2007.14544",
  "version": "v1",
  "published": "2020-07-29T01:06:07.000Z",
  "updated": "2020-07-29T01:06:07.000Z",
  "title": "Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds",
  "authors": [
    "Hisashi Kasuya"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DG",
    "math.AG",
    "math.AT"
  ],
  "abstract": "For a $2n+1$-dimensional compact Sasakian manifold, if $n\\ge 2$, we prove that the analytic germ of the variety of representations of the fundamental group at every semi-simple representation is quadratic. To prove this result, we prove the almost-formality of de Rham complex of a Sasakian manifold with values in a semi-simple flat vector bundle. By the almost-formality, we also prove the vanishing theorem on the cup product of the cohomology of semi-simple flat vector bundles over a compact Sasakian manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-29T01:06:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental group",
      "semi-simple flat vector bundle",
      "almost-formality",
      "deformations",
      "dimensional compact sasakian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}