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

Compactified Twistor Fibration and Topology of Ward Unitons