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. 391–414DOI 10.4171/GGD/231