{
  "id": "1609.07805",
  "version": "v1",
  "published": "2016-09-25T21:28:33.000Z",
  "updated": "2016-09-25T21:28:33.000Z",
  "title": "$L^2$-Euler characteristics and the Thurston norm",
  "authors": [
    "Stefan Friedl",
    "Wolfgang Lück"
  ],
  "comment": "42 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We assign to a finite $CW$-complex and an element in its first cohomology group a twisted version of the $L^2$-Euler characteristic and study its main properties. In the case of an irreducible orientable $3$-manifold with empty or toroidal boundary and infinite fundamental group we identify it with the Thurston norm. We will use the $L^2$-Euler characteristic to address the problem whether the existence of a map inducing an epimorphism on fundamental groups implies an inequality of the Thurston norms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-25T21:28:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thurston norm",
      "euler characteristic",
      "first cohomology group",
      "infinite fundamental group",
      "fundamental groups implies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}