  A divide is a relative generic immersion of a finite union of copies of the
unit interval in the unit disk. A divide defines a classical link in the 3-
sphere, which is a fibered link if the image of the immersion is connected. We
prove in this paper, that the Lefschetz number of the monodromy is 0. This
result was known for divides, which correspond to real morsifications of
complexe plane curve singularities. The proof uses the space of gradient lines
of a morse function.
