{
  "id": "math/9810172",
  "version": "v2",
  "published": "1998-10-29T21:16:39.000Z",
  "updated": "1998-11-19T19:50:38.000Z",
  "title": "Volume of Riemannian manifolds, geometric inequalities, and homotopy theory",
  "authors": [
    "Mikhail G. Katz",
    "Alexander I. Suciu"
  ],
  "comment": "25 pages, LaTeX2e, 3 figures. To appear in the Rothenberg Festschrift, Contemporary Math",
  "journal": "Tel Aviv Topology Conference: Rothenberg Festschrift (1998), 113-136, Contemp. Math., vol. 231, Amer. Math. Soc., Providence, RI, 1999",
  "categories": [
    "math.DG",
    "math.AT"
  ],
  "abstract": "We outline the current state of knowledge regarding geometric inequalities of systolic type, and prove new results, including systolic freedom in dimension 4. Namely, every compact, orientable, smooth 4-manifold X admits metrics of arbitrarily small volume such that every orientable, immersed surface of smaller than unit area is necessarily null-homologous in X.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1998-11-19T19:50:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23",
      "55Q15"
    ],
    "keywords": [
      "riemannian manifolds",
      "homotopy theory",
      "knowledge regarding geometric inequalities",
      "current state",
      "arbitrarily small volume"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....10172K"
    }
  }
}