Vol. 238, No. 1, 2008

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ISSN: 0030-8730
Unfaithful complex hyperbolic triangle groups, I: Involutions

John Robert Parker

Vol. 238 (2008), No. 1, 145–169

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.

complex hyperbolic geometry, triangle groups
Mathematical Subject Classification 2000
Primary: 20H10, 22E40, 51M10
Received: 28 November 2007
Revised: 18 June 2008
Accepted: 1 July 2008
Published: 1 November 2008
John Robert Parker
Department of Mathematical Sciences
Durham University
South Road
Durham DH1 3LE
United Kingdom