additional smoothing filter which in our case has been used during the stereographic projection. We use $N_\ell$ as the average noise power spectrum derived from the noise power model given in Hinshaw et al. (2003). The theoretical genus amplitudes expected from the WMAP power spectrum are $A=866$, $1313$, and $2034$ for Q, V, and W bands, respectively, and are very similar to those from mock observations.

Genus in Northern and Southern Hemispheres
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As we have shown in the previous section, the CMB temperature fluctuation measured by the WMAP appears to be consistent with Gaussian random phase field. However, the temperature distributions of the Galactic northern and southern hemispheres look very different with each other, especially due to the presence of large cold spots near the Galactic plane in the southern hemisphere (see Fig. 4). There are two big cold spots near $(\ell,b) \approx (330\degr, -10\degr)$ and $(200\degr,-20\degr)$. Figures 4$b$ and 4$c$ compare the temperature distributions of the ILC northern and southern hemispheres, showing that both are quite different from each other.

![image](jfig4a_m.eps){width="140mm"} ![image](jfig4bc_m.eps){width="140mm"}

The northern hemisphere has very few big spots while the southern hemisphere has many.

We calculate the genus separately from the northern and the southern parts 