{
  "id": "math/0103183",
  "version": "v2",
  "published": "2001-03-27T15:28:33.000Z",
  "updated": "2001-12-24T19:28:58.000Z",
  "title": "Equivariant framings, lens spaces and Contact structures",
  "authors": [
    "Siddhartha Gadgil"
  ],
  "comment": "10 pages, to appear in the Pacific Journal of Mathematics",
  "categories": [
    "math.GT"
  ],
  "abstract": "We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong enough to yield the classification of lens spaces of odd, prime order. We also use properties of this invariant to show that there is an oriented 3-manifold with no universally tight contact structure. We generalise and sharpen this invariant to an invariant of a finite covering of a 3-manifold.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-12-24T19:28:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M60",
      "57M27"
    ],
    "keywords": [
      "lens spaces",
      "equivariant framings",
      "universally tight contact structure",
      "tangent bundle",
      "prime order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......3183G"
    }
  }
}