{
  "id": "1312.0823",
  "version": "v2",
  "published": "2013-12-03T13:54:29.000Z",
  "updated": "2014-08-18T10:14:25.000Z",
  "title": "Sutured Floer homology, fibrations, and taut depth one foliations",
  "authors": [
    "Irida Altman",
    "Stefan Friedl",
    "András Juhász"
  ],
  "comment": "30 pages, improved exposition",
  "categories": [
    "math.GT"
  ],
  "abstract": "For an oriented irreducible 3-manifold M with non-empty toroidal boundary, we describe how sutured Floer homology ($SFH$) can be used to determine all fibered classes in $H^1(M)$. Furthermore, we show that the $SFH$ of a balanced sutured manifold $(M,\\gamma)$ detects which classes in $H^1(M)$ admit a taut depth one foliation such that the only compact leaves are the components of $R(\\gamma)$. The latter had been proved earlier by the first author under the extra assumption that $H_2(M)=0$. The main technical result is that we can obtain an extremal $\\text{Spin}^c$-structure $\\mathfrak{s}$ (i.e., one that is in a `corner' of the support of $SFH$) via a nice and taut sutured manifold decomposition even when $H_2(M) \\neq 0$, assuming the corresponding group $SFH(M,\\gamma,\\mathfrak{s})$ has non-trivial Euler characteristic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-18T10:14:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57R58"
    ],
    "keywords": [
      "sutured floer homology",
      "taut depth",
      "fibrations",
      "non-empty toroidal boundary",
      "taut sutured manifold decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.0823A"
    }
  }
}