  We use the compactified twistor correspondence for the (2+1)-dimensional
integrable chiral model to prove a conjecture of Ward. In particular, we
construct the correspondence space of a compactified twistor fibration and use
it to prove that the second Chern numbers of the holomorphic vector bundles,
corresponding to the uniton solutions of the integrable chiral model, equal the
third homotopy classes of the restricted extended solutions of the unitons.
Therefore we deduce that the total energy of a time-dependent uniton is
proportional to the second Chern number.
