On the algebraic convergence of finitely generated Kleinian groups

Authors

  • Xi Fu

Keywords:

Kleinian group, loxodromic element

Abstract

Let $\{G_{r,i}\}$ be a sequence of $r$-generator Kleinian groups acting on $\mathbb{\overline{R}}^n$. In this paper, we prove that if $\{G_{r,i}\}$ satisfies $F$-condition, then its algebraic limit group $G_r$ is also a Kleinian group. The existence of a homomorphism from $G_r$ to $G_{r,i}$ is also proved. These are generalizations of all known corresponding results. DOI: 10.1017/S0004972711003017

Published

2012-02-27

Issue

Vol. 85 No. 2 (2012)

Section

Articles
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