#### Vol. 294, No. 1, 2018

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Three-dimensional Sol manifolds and complex Kleinian groups

### Waldemar Barrera, Rene Garcia-Lara and Juan Navarrete

Vol. 294 (2018), No. 1, 1–18
##### Abstract

We give a topological description of the quotient space $\Omega \left(G\right)∕G$, in the case when is a discrete subgroup acting on ${ℙ}_{ℂ}^{2}$ and the maximum number of complex projective lines in general position contained in the Kulkarni limit set $\Lambda \left(G\right)={ℙ}_{ℂ}^{2}\setminus \Omega \left(G\right)$ is equal to 4. Moreover, we give a topological description of the quotient space $\Omega \left(G\right)∕G$ in the case when $G$ is a lattice of the Heisenberg group.

##### Keywords
Kleinian groups, projective complex plane, discrete groups, limit set
##### Mathematical Subject Classification 2010
Primary: 32F45, 37F30, 32Q45
Secondary: 22E40, 37F45