{
  "id": "1804.09519",
  "version": "v1",
  "published": "2018-04-25T12:36:24.000Z",
  "updated": "2018-04-25T12:36:24.000Z",
  "title": "Sutured manifolds and $L^2$-Betti numbers",
  "authors": [
    "Gerrit Herrmann"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "Using the virtual fibering theorem of Agol we show that a sutured 3-manifold $(M, R_+,R_-,\\gamma)$ is taut if and only if the $\\ell^2$-Betti numbers of the pair $(M,R_-)$ are zero. As an application we can characterize Thurston norm minimizing surfaces in a 3-manifold $N$ with empty or toroidal boundary by the vanishing of certain $\\ell^2$-Betti numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-25T12:36:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "betti numbers",
      "sutured manifolds",
      "characterize thurston norm minimizing surfaces",
      "virtual fibering theorem",
      "toroidal boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}