Unfaithful complex hyperbolic triangle groups I: Involutions

Parker, John R.

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.

Citation

Parker, J. R. (2008). Unfaithful complex hyperbolic triangle groups I: Involutions. Pacific Journal of Mathematics, 238(1), 145-169. https://doi.org/10.2140/pjm.2008.238.145

• Journal Article Type: Article
• Publication Date: Nov 1, 2008
• Deposit Date: Oct 29, 2009
• Publicly Available Date: Dec 1, 2017
• Journal: Pacific Journal of Mathematics
• Publisher: Mathematical Sciences Publishers (MSP)
• Peer Reviewed: Peer Reviewed
• Volume: 238
• Issue: 1
• Pages: 145-169
• DOI: https://doi.org/10.2140/pjm.2008.238.145
• Keywords: Complex hyperbolic geometry, Triangle group.
• Publisher URL: http://pjm.berkeley.edu/pjm/2008/238-1/p08.xhtml