As continuation of this question consider subset
$N^4=\{Re(x^p+y^q+z^r)=0:x,y,z\in\mathbb C, |x|^2+|y|^2+|z|^2=1\}$
in sphere $S^5$. It is 4-manifold in sphere which contains Brieskorn $\Sigma(p,q,r)$ as submanifold. Is it possible to calculate homology groups of N ? Is it homology 4-sphere ?