Distortions with double topological character : the case of cholesterics

The topological classification of distortions in ordered media leads naturally to a distinction'between singular distortions (defects) and non singular distortions. However, in cholesteric liquid crystals, where the order parameter contains components with different rigidities, the optically observed distortions present both singular and non singular aspects : they have a double topological character. This phenomenon, which is predicted to exist also in other ordered systems, is analysed here in terms of the Hopf index for a director field.