  We study the complex of partial bases of a free group, which is an analogue
for $\Aut(F_n)$ of the curve complex for the mapping class group. We prove that
it is connected and simply connected, and we also prove that its quotient by
the Torelli subgroup of $\Aut(F_n)$ is highly connected. Using these results,
we give a new, topological proof of a theorem of Magnus that asserts that the
Torelli subgroup of $\Aut(F_n)$ is finitely generated.
