Geometric limits of quasi-Fuchsian groups

TL;DR

This paper characterizes the topological types of hyperbolic 3-manifolds arising as geometric limits of algebraically convergent sequences of quasi-Fuchsian groups, advancing understanding of their geometric and topological properties.

Contribution

It provides a classification of hyperbolic 3-manifolds that can be obtained as geometric limits of quasi-Fuchsian groups, a novel result in geometric group theory.

Findings

Identifies possible topological types of hyperbolic 3-manifolds as geometric limits.

Connects algebraic convergence of groups with geometric limits.

Enhances understanding of the structure of quasi-Fuchsian groups.

Abstract

In this paper, we will determine the topological types of hyperbolic 3-anifolds H^3/G such that G is a geometric limit of any algebraically convergent sequence of quasi-Fuchsian groups.