  In 1981, Arnoux and Yoccoz gave the first examples of pseudo-Anosov maps with
odd degree stretch factors. In 1985, D.~Fried deduced the existence of a
pseudo-Anosov map in genus three with the same stretch factor as the
Arnoux-Yoccoz example in that genus, and asked if these were the same. We show
that they are distinct. We do this by, in a sense, reversing Fried's
construction; we show that the mapping torus of the pseudo-Anosov map induced
by the Arnoux-Yoccoz map on the surface obtained by blowing-up its two
singularities has no cross section which is a torus with two points blown-up.
