  Las Vergnas introduced several lattice structures on the bases of an ordered
matroid M by using their external and internal activities. He also noted that
when computing the Moebius function of these lattices, it was often zero,
although he had no explanation for that fact. The purpose of this paper is to
provide a topological reason for this phenomenon. In particular, we show that
the order complex of the external lattice L of M is homotopic to the
independence complex of the restriction M^*|T where M^* is the dual of M and T
is the top element of L. We then compute some examples showing that this latter
complex is often contractible which forces all its homology groups, and thus
its Moebius function, to vanish. A theorem of Bj\"orner also helps us to
calculate the homology of the matroid complex.
