  The topology of the non-adiabatic parameter space bundle is discussed for
evolution of exact cyclic state vectors in Berry's original example of split
angular momentum eigenstates. It turns out that the change in topology occurs
at a critical frequency. The first Chern number that classifies these bundles
is proportional to angular momentum. The non-adiabatic principal bundle over
the parameter space is not well-defined at the critical frequency.
