One line complex Kleinian groups

Waldemar Barrera, Angel Cano and Juan Pablo Navarrete

Vol. 272 (2014), No. 2, 275–303

DOI: 10.2140/pjm.2014.272.275

Abstract

We give an algebraic description of those subgroups of $PGL\left(3,ℂ\right)$ acting on ${\mathbb{P}}_{ℂ}^2$ with Kulkarni limit set equal to one complex projective line. Conversely, we prove that the Kulkarni limit set of a group $G\le PGL\left(3,ℂ\right)$ acting properly and discontinuously on the complement of one line in ${\mathbb{P}}_{ℂ}^2$ is equal to one or two lines.

Keywords

complex Kleinian groups, Kulkarni limit set, complex projective plane

Mathematical Subject Classification 2010

Primary: 37F30, 22E40

Milestones

Received: 26 September 2013

Revised: 17 December 2013

Accepted: 10 March 2014

Published: 28 November 2014