# Three-dimensional sol manifolds and complex kleinian groups

## TL;DR

This paper explores the topology of quotient spaces formed by discrete subgroups acting on complex projective planes, focusing on complex Kleinian groups and Heisenberg lattices, with results on the maximum number of lines in limit sets.

## Contribution

It provides a topological description of quotient spaces for specific complex Kleinian groups and Heisenberg lattices, highlighting the maximum number of lines in limit sets.

## Key findings

- Maximum of 4 complex lines in Kulkarni's limit set for certain groups
- Topological descriptions of quotient spaces for these groups
- Characterization of limit sets in complex projective geometry

## Abstract

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