  We apply the Bogomol'nyi technique, which is usually invoked in the study of
solitons or models with topological invariants, to the case of elastic energy
of vesicles. We show that spontaneous bending contribution caused by any
deformation from metastable bending shapes falls in two distinct topological
sets: shapes of spherical topology and shapes of non-spherical topology
experience respectively a deviatoric bending contribution a la Fischer and a
mean curvature bending contribution a la Helfrich. In other words, topology may
be considered to describe bending phenomena. Besides, we calculate the bending
energy per genus and the bending closure energy regardless of the shape of the
vesicle. As an illustration we briefly consider geometrical frustration
phenomena experienced by magnetically coated vesicles.
