  We show that the complex of free factors of a free group of rank n > 1 is
homotopy equivalent to a wedge of spheres of dimension n-2. We also prove that
for n > 1, the complement of (unreduced) Outer space in the free splitting
complex is homotopy equivalent to the complex of free factor systems and
moreover is (n-2)-connected. In addition, we show that for every non-trivial
free factor system of a free group, the corresponding relative free splitting
complex is contractible.
