{
  "id": "2103.09997",
  "version": "v1",
  "published": "2021-03-18T03:09:34.000Z",
  "updated": "2021-03-18T03:09:34.000Z",
  "title": "Lower Bound for the Simplicial Volume of Closed Manifolds Covered by $\\mathbb{H}^{2}\\times\\mathbb{H}^{2}\\times\\mathbb{H}^{2}$",
  "authors": [
    "Jixiang Fu",
    "Xiaofeng Meng"
  ],
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We estimate the upper bound for the $\\ell^{\\infty}$-norm of the volume form on $\\mathbb{H}^2\\times\\mathbb{H}^2\\times\\mathbb{H}^2$ seen as a class in $H_{c}^{6}(\\mathrm{PSL}_{2}\\mathbb{R}\\times\\mathrm{PSL}_{2}\\mathbb{R}\\times\\mathrm{PSL}_{2}\\mathbb{R};\\mathbb{R})$. This gives the lower bound for the simplicial volume of closed Riemennian manifolds covered by $\\mathbb{H}^{2}\\times\\mathbb{H}^{2}\\times\\mathbb{H}^{2}$. The proof of these facts yields an algorithm to compute the lower bound of closed Riemannian manifolds covered by $\\big(\\mathbb{H}^2\\big)^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-18T03:09:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bound",
      "simplicial volume",
      "closed manifolds",
      "closed riemannian manifolds",
      "facts yields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}