To make the genus amplitudes for the mock observations similar to those for the observed WMAP maps, we use the unbinned WMAP power spectrum (Spergel et al. 2003) at low $\ell$’s ($\le 342$) and the CMBFAST-generated power spectrum (Seljak & Zaldarriaga 1996) that fits the WMAP power spectrum together with the CBI and ACBAR results at high $\ell$’s ($> 342$). For each mock observation, the same initial condition for $a_{\ell m}$’s is used for all frequency channels, where $a_{\ell m}$’s are coefficients in spherical harmonic expansion of the temperature anisotropy field. During the map generation, the WMAP beam transfer function $B_\ell$ is used for each differencing assembly, and the instrument noise at each pixel is randomly drawn from the Gaussian distribution with variance of $\sigma_0^2/N_{\rm obs}$. The average genus measured from the 500 mock WMAP observations are shown in Figure 2.

The genus-related statistics for the 500 mock observations are listed in Table 2, where the mean and standard deviation for each genus-related parameter are shown. Due to the complex noise property in the WMAP data, the genus shift parameters have means far deviating from zero, with $\Delta\nu_{-}$ and $\Delta\nu_{+}$ having opposite signs with each other. Figure 3 shows the 