in equation (3), and likewise for $A_{+}^{\rm N(S)}$. The $A_{-/+}^{\rm N} - A_{-/+}^{\rm S}$ have non-zero mean values even for the Gaussian mock observations. The measured value $A_{-}^{\rm N} - A_{-}^{\rm S} = 255$ for the W band map is 2.6 times larger than the standard deviation of those expected from the simulated Gaussian observations ($[255-17]/90 \simeq 2.6$). On the other hand, $A_{+}^{\rm N} - A_{+}^{\rm S}$ has smaller value due to the large genus asymmetry ($\Delta g$) in the south.

We also have measured $A_{-/+}^{\rm N} - A_{-/+}^{\rm S}$ from the WMAP Q and V band maps, TCM, and ILC. From Table 3, we find that the large genus amplitude difference between the north and the south also appear at both Q and V bands (Fig. 5$b$ and 5$c$), deviating the Gaussian prediction with significance levels of about $2\sigma$ ($A_{-/+}^{\rm N} - A_{-/+}^{\rm S} = 1.9\sigma$ – $2.0\sigma$), which shows that this non-Gaussian feature does not have any frequency dependence. We have computed a probability of finding such a significant deviation from the Gaussian prediction in the mock WMAP CMB fields with the Gaussian statistics. The probability that the genus curves show such a large genus amplitude differences exceeding 