Abstract
A topological approach in the HR diagram is given for the occurrence and the characteristics of convective envelopes in population II stars. The location of the Hayashi track and of the Red Giants branch are both investigated for various assumed masses of the stars and chemical compositions of the convective layers. An analysis is performed on the influence of the assumed mixing length. The observational consequences of a possible mass loss is discussed for both the Red Giants and the Asymptotic branches. Possible causes for separation between these two branches are briefly examined. The case of the globular cluster ω Cen is investigated, in order to give some suggestions for a large dispersion in colours observed among the giants belonging to this cluster.
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