{
  "id": "0711.4337",
  "version": "v2",
  "published": "2007-11-27T19:52:00.000Z",
  "updated": "2009-02-22T23:56:01.000Z",
  "title": "Intersection form, laminations and currents on free groups",
  "authors": [
    "Ilya Kapovich",
    "Martin Lustig"
  ],
  "comment": "revised version, to appear in GAFA",
  "journal": "Geom. Funct. Anal. vol. 19 (2010), no. 5, pp. 1426-1467",
  "doi": "10.1007/s00039-009-0041-3",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "Let $F_N$ be a free group of rank $N\\ge 2$, let $\\mu$ be a geodesic current on $F_N$ and let $T$ be an $\\mathbb R$-tree with a very small isometric action of $F_N$. We prove that the geometric intersection number $<T, \\mu>$ is equal to zero if and only if the support of $\\mu$ is contained in the dual algebraic lamination $L^2(T)$ of $T$. Applying this result, we obtain a generalization of a theorem of Francaviglia regarding length spectrum compactness for currents with full support. As another application, we define the notion of a \\emph{filling} element in $F_N$ and prove that filling elements are \"nearly generic\" in $F_N$. We also apply our results to the notion of \\emph{bounded translation equivalence} in free groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-02-22T23:56:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free group",
      "intersection form",
      "francaviglia regarding length spectrum compactness",
      "dual algebraic lamination",
      "geometric intersection number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.4337K"
    }
  }
}