  We present properties of the peaks (maxima) of the CMB anisotropies expected
in flat and open CDM models. We obtain analytical expressions of several
topological descriptors: mean number of maxima and the probability distribution
of the gaussian curvature and the eccentricity of the peaks. These quantities
are calculated as functions of the radiation power spectrum, assuming a
gaussian distribution of temperature anisotropies. We present results for
angular resolutions ranging from 5' to 20' (antenna FWHM), scales that are
relevant for the MAP and COBRAS/SAMBA space missions and the ground-based
interferometer experiments. Our analysis also includes the effects of noise. We
find that the number of peaks can discriminate between standard CDM models, and
that the gaussian curvature distribution provides a useful test for these
various models, whereas the eccentricity distribution can not distinguish
between them.
