Three-dimensional sol manifolds and complex kleinian groups

We give a topological description of the quotient space $\mathrm{\Omega }(G)\mathrm{/}G$ in the case $G\subset PSL(3,\mathbb{C})$ is a discrete subgroup acting on ${\mathbb{P}}_{\mathbb{C}}^2$ and the maximum number of complex projective lines in general position contained in Kulkarni’s limit set, $\mathrm{\Lambda }(G)$, is 4. We also give a topological description of the quotient space $\mathrm{\Omega }(G)\mathrm{/}G$ in the case $G$ a lattice of Heisenberg’s group.