{
  "id": "math/0611149",
  "version": "v2",
  "published": "2006-11-06T18:44:21.000Z",
  "updated": "2006-11-21T16:23:31.000Z",
  "title": "A function on the homology of 3-manifolds",
  "authors": [
    "Vladimir Turaev"
  ],
  "comment": "16 pages, no figures. The second version incorporates several minor corrections",
  "categories": [
    "math.GT"
  ],
  "abstract": "In analogy with the Thurston norm, we define for an orientable 3-manifold $M$ a numerical function on $H_2(M;Q/Z)$. This function measures the minimal complexity of folded surfaces representing a given homology class. A similar function is defined on the torsion subgroup of $H_1(M)$. These functions are estimated from below in terms of abelian torsions of $M$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-11-21T16:23:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99"
    ],
    "keywords": [
      "torsion subgroup",
      "thurston norm",
      "similar function",
      "homology class",
      "function measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11149T"
    }
  }
}