The complex of partial bases for F_n and finite generation of the Torelli subgroup of Aut(F_n) (with M. Day) - [pdf] [ps]
to appear in Geom. Dedicata.
Abstract :
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.