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 from the Handel–Mosher proof of hyperbolicity of the free splitting complex of , thus obtaining an alternative proof of a theorem of Bestvina–Feighn. We also show that under the natural map from the free splitting complex to free factor complex, a geodesic maps to a path that is uniformly Hausdorff-close to a geodesic .

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