{
  "id": "0903.1094",
  "version": "v2",
  "published": "2009-03-05T20:36:41.000Z",
  "updated": "2009-09-22T23:51:36.000Z",
  "title": "Dihedral manifold approximate fibrations over the circle",
  "authors": [
    "Bruce Hughes",
    "Qayum Khan"
  ],
  "comment": "39 pages",
  "journal": "Geometriae Dedicata, Volume 148, Issue 1 (2010), 205-243",
  "doi": "10.1007/s10711-009-9418-6",
  "categories": [
    "math.GT"
  ],
  "abstract": "Consider the cyclic group C_2 of order two acting by complex-conjugation on the unit circle S^1. The main result is that a finitely dominated manifold W of dimension > 4 admits a cocompact, free, discontinuous action by the infinite dihedral group D_\\infty if and only if W is the infinite cyclic cover of a free C_2-manifold M such that M admits a C_2-equivariant manifold approximate fibration to S^1. The novelty in this setting is the existence of codimension-one, invariant submanifolds of M and W. Along the way, we develop an equivariant sucking principle for certain orthogonal actions of finite groups on Euclidean space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-22T23:51:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N15",
      "57S30"
    ],
    "keywords": [
      "dihedral manifold approximate fibrations",
      "infinite cyclic cover",
      "infinite dihedral group",
      "unit circle",
      "equivariant sucking principle"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1094H"
    }
  }
}