{
  "id": "1309.1511",
  "version": "v4",
  "published": "2013-09-05T23:42:06.000Z",
  "updated": "2014-06-05T17:14:21.000Z",
  "title": "Virtual Homological Torsion of Closed Hyperbolic 3-manifolds",
  "authors": [
    "Hongbin Sun"
  ],
  "comment": "23 pages, 2 figures, some minor mistake on page 21 was corrected, thanks for the referee for valuable suggestions",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we will use Kahn-Markovic's almost totally geodesic surfaces to construct certain $\\pi_1$-injective 2-complexes in closed hyperbolic 3-manifolds. Such 2-complexes are locally almost totally geodesic except along a 1-dimensional subcomplex. Using Agol and Wise's result that fundamental groups of hyperbolic 3-manifolds are LERF and quasi-convex subgroups are virtual retract, we will show that closed hyperbolic 3-manifolds virtually contain any prescribed homological torsion: For any finite abelian group $A$, and any closed hyperbolic 3-manifold $M$, there exists a finite cover $N$ of $M$, such that $A$ is a direct summand of $Tor(H_1(N;\\mathbb{Z}))$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-06-05T17:14:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M10",
      "57M50",
      "30F40"
    ],
    "keywords": [
      "closed hyperbolic",
      "virtual homological torsion",
      "finite abelian group",
      "direct summand",
      "totally geodesic surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1511S"
    }
  }
}