  We study the group of C^{r}-diffeomorphisms of the closed annulus that are
isotopic to the identity. We show that, for r different from 3, the linear
space of homogeneous quasi-morphisms on this group is one dimensional.
Therefore, the commutator length on this group is (stably) unbounded. In
particular, this provides an example of a manifold whose diffeomorphisms group
is unbounded in the sense of Burago, Ivanov and Polterovich.
