{
  "id": "1904.04539",
  "version": "v1",
  "published": "2019-04-09T08:51:26.000Z",
  "updated": "2019-04-09T08:51:26.000Z",
  "title": "The spectrum of simplicial volume",
  "authors": [
    "Nicolaus Heuer",
    "Clara Loeh"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of simplicial volumes of orientable closed connected manifolds is dense in $\\mathbb{R}_{\\geq 0}$. In dimension 4 we prove that every non-negative rational number is the simplicial volume of some orientable closed connected 4-manifold. Our group theoretic results relate stable commutator length to the $l^1$-semi-norm of certain singular homology classes in degree 2. The output of these results is translated into manifold constructions using cross-products and Thom realisation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-09T08:51:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N65",
      "57M07",
      "20J05"
    ],
    "keywords": [
      "simplicial volume",
      "results relate stable commutator length",
      "theoretic results relate stable commutator",
      "manufacture high-dimensional manifolds",
      "group theoretic results relate stable"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}