On the number of lines in the limit set for discrete subgroups of $\operatorname{PSL}(3,\mathbb{C})$

Waldemar Barrera, Angel Cano and Juán Navarrete

Vol. 281 (2016), No. 1, 17–49

DOI: 10.2140/pjm.2016.281.17

Abstract

Given a discrete subgroup $G\subset PSL\left(3,ℂ\right)$, acting on the complex projective plane, ${\mathbb{P}}_{ℂ}^2$, in the canonical way, we list all possible values for the number of complex projective lines and for the maximum number of complex projective lines lying in the complement of each of: the equicontinuity set of $G$, the Kulkarni discontinuity region of $G$, and maximal open subsets of ${\mathbb{P}}_{ℂ}^2$ on which $G$ acts properly discontinuously.

Keywords

Kleinian groups, projective complex plane, discrete groups, limit set

Mathematical Subject Classification 2010

Primary: 32Q45, 37F30

Secondary: 37F45, 22E40

Milestones

Received: 19 December 2014

Revised: 14 July 2015

Accepted: 20 July 2015

Published: 9 February 2016