{
  "id": "1911.01801",
  "version": "v1",
  "published": "2019-11-05T14:33:33.000Z",
  "updated": "2019-11-05T14:33:33.000Z",
  "title": "Geometric construction of homology classes in Riemannian manifolds covered by products of the hyperbolic plane",
  "authors": [
    "Pascal Zschumme"
  ],
  "comment": "20 pages, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study the homology of Riemannian manifolds of finite volume that are covered by a product $(\\mathbb{H}^2)^r = \\mathbb{H}^2 \\times \\ldots \\times \\mathbb{H}^2$ of the real hyperbolic plane. Using a variation of a method developed by Avramidi and Nyguen-Phan, we show that any such manifold $M$ possesses, up to finite coverings, an arbitrarily large number of compact oriented flat totally geodesic $r$-dimensional submanifolds whose fundamental classes are linearly independent in the real homology group $H_r(M;\\mathbb{R})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-05T14:33:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57T99",
      "11F75",
      "22E40",
      "53C35"
    ],
    "keywords": [
      "riemannian manifolds",
      "homology classes",
      "geometric construction",
      "real homology group",
      "compact oriented flat totally geodesic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}