Unfaithful complex hyperbolic triangle groups, I: Involutions

John Robert Parker

Vol. 238 (2008), No. 1, 145–169

DOI: 10.2140/pjm.2008.238.145

Abstract

A complex hyperbolic triangle group is the group of complex hyperbolic isometries generated by complex involutions fixing three complex lines in complex hyperbolic space. Such a group is called equilateral if there is an isometry of order three that cyclically permutes the three complex lines. We consider equilateral triangle groups for which the product of each pair of involutions and the product of all three involutions are all nonloxodromic. We classify all such groups that are discrete.

Keywords

complex hyperbolic geometry, triangle groups

Mathematical Subject Classification 2000

Primary: 20H10, 22E40, 51M10

Milestones

Received: 28 November 2007

Revised: 18 June 2008

Accepted: 1 July 2008

Published: 1 November 2008