The hyperbolicity of the sphere complex via surgery paths
  Handel and Mosher have proved that the free splitting complex FS for the free group is Gromov hyperbolic. This is a deep and much sought-after result, since it establishes FS as a good analogue of the curve complex for surfaces.   We give a shorter alternative proof of this theorem, using surgery paths in Hatcher's sphere complex (another model for the free splitting complex), instead of Handel and Mosher's fold paths. As a byproduct, we get that surgery paths are unparameterized quasi-geodesics in the sphere complex.   We explain how to deduce from our proof the hyperbolicity of some other complexes such as the free factor complex or the arc complex (of a surface with boundary). 
Arnaud Hilion, Camille Horbez
math.GT math.GR