On hyperbolicity of free splitting and free factor complexes

  • Ilya Kapovich

    University of Illinois at Urbana-Champaign, USA
  • Kasra Rafi

    University of Oklahoma, Norman, USA

Abstract

We show how to derive hyperbolicity of the free factor complex of FNF_N from the Handel–Mosher proof of hyperbolicity of the free splitting complex of FNF_N, thus obtaining an alternative proof of a theorem of Bestvina–Feighn. We also show that under the natural map τ\tau from the free splitting complex to free factor complex, a geodesic [x,y][x,y] maps to a path that is uniformly Hausdorff-close to a geodesic [τ(x),τ(y)][\tau(x),\tau(y)].

Cite this article

Ilya Kapovich, Kasra Rafi, On hyperbolicity of free splitting and free factor complexes. Groups Geom. Dyn. 8 (2014), no. 2, pp. 391–414

DOI 10.4171/GGD/231