{
  "id": "0809.4446",
  "version": "v1",
  "published": "2008-09-25T16:24:36.000Z",
  "updated": "2008-09-25T16:24:36.000Z",
  "title": "Bounded Cohomology and $l_1$-Homology of Three-Manifolds",
  "authors": [
    "P. Derbez"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we define, for each aspherical orientable 3-manifold $M$ endowed with a \\emph{torus splitting} $\\c{T}$, a 2-dimensional fundamental $l_1$-class $[M]^{\\c{T}}$ whose $l_1$-norm has similar properties as the Gromov simplicial volume of $M$ (additivity under torus splittings and isometry under finite covering maps). Next, we use the Gromov simplicial volume of $M$ and the $l_1$-norm of $[M]^{\\c{T}}$ to give a complete characterization of those nonzero degree maps $f\\co M\\to N$ which are homotopic to a ${\\rm deg}(f)$-covering map. As an application we characterize those degree one maps $f\\co M\\to N$ which are homotopic to a homeomorphism in terms of bounded cohomology classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-25T16:24:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "51H20"
    ],
    "keywords": [
      "gromov simplicial volume",
      "three-manifolds",
      "nonzero degree maps",
      "similar properties",
      "bounded cohomology classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4446D"
    }
  }
}