  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).
